Washington (CNN) -- Despite a ballyhooed charm offensive by President Barack Obama, political leaders continued talking past each other on Tuesday in proposing partisan ideas on taxes and spending that have zero chance of winning congressional approval.
Obama met with Senate Democrats in the first of three visits to Capitol Hill this week for face time with legislators from both parties.
The rare personal appearances by the president, a former senator, follow his newly unveiled outreach efforts that included dinner with Senate Republicans and lunch with two influential House members last week, as well as phone calls to various legislators from both parties.
Obama offered no comment to reporters when entering and departing Tuesday's meeting with senators, while White House spokesman Jay Carney rejected any inference that the meetings and phone calls by the president were just for show.
Democratic senators who met with Obama described him as upbeat and supportive.
Sen. Carl Levin of Michigan said Obama called compromise with Republicans essential, but added that the president acknowledged "he hasn't seen enough from them yet."
Another participant, Sen. Ben Cardin of Maryland, said Obama stayed longer than expected to answer "about a dozen questions" on fiscal issues and other topics, noting that he "obviously wanted to be there."
The top Senate Republican, Mitch McConnell of Kentucky, said he welcomed Obama's efforts, adding: "I think having more of that rather than less of that is a good idea."
Democratic senators who met with Obama on Tuesday described the president as upbeat and supportive.
Whether symbolic or sincere, Obama's increased personal engagement came as Congress prepared for the first formal budget debate since the president took office four years ago.
However, all signs Tuesday indicated the issues and rhetoric would be much the same as during the repeated political showdowns that marked the president's first term.
House Budget Committee Chairman Paul Ryan fired the opening salvo, introducing a conservative budget proposal for fiscal year 2014 that he said would eliminate the annual deficit in a decade without raising taxes.
"We think we owe the country a balanced budget," Ryan told reporters. "We think we owe the country solutions to the big problems that are plaguing our nation -- a debt crisis on the horizon, a slow growing economy, people trapped in poverty. We are showing our answers."
The Wisconsin Republican's plan calls for cutting $5 trillion from projected spending increases in the next 10 years while lowering tax rates and getting rid of most of Obama's signature legislation of his first term -- the 2010 health care reform law.
Ryan also revived his controversial proposal to reform Medicare, the health care program for senior citizens that is considered the biggest driver of rising federal deficits as costs increase and more Americans become eligible.
The idea was a major issue in last year's presidential election, in which Ryan was the vice presidential candidate on the GOP ticket that lost to Obama.
It calls for offering senior citizens a choice between traditional fee-for-service Medicare and a premium support system that would provide a fixed government payment to help them buy private health insurance. The plan would take effect in 2024 to exempt people 55 and older today.
Democratic rejection of much of Ryan's approach was swift with the White House saying that his math didn't add up, using language from policy debates of last year's election campaign.
"If instead of asking the wealthiest to contribute to deficit reduction, you say we'd like to give the wealthiest a huge tax cut, the result is that ... the burden is doubled or tripled on everyone else and that just doesn't seem fair and it's also not good economics," presidential spokesman Jay Carney told reporters.
Obama followed up.
"We're not going to balance the budget in 10 years," he said in an interview with ABC News. "If you look at what Paul Ryan does to balance the budget, it means that you have to 'voucherize' Medicare, you have to slash deeply into programs like Medicaid, you've essentially got to either tax middle class families a lot higher than you currently are or you can't lower rates the way he's promised."
Senate Majority Leader Harry Reid, D-Nevada, contended that Ryan's proposal was "even more extreme" than Republican policies rejected by voters in the November election.
For his part, Ryan noted that "the election didn't go our way," but asked whether that meant Republicans must surrender their principles.
However, he sounded contradictory when challenged about his call to eliminate most of Obama's health care reform law. After first saying "we are not going to re-fight the past" and that "law is law" with regard to the measure known as Obamacare, Ryan later said that "we need to repeal and replace Obamacare with a better system."
Senate Democrats plan to make public their own 2014 budget proposal on Wednesday, and Reid confirmed it would call for an equal amount of increased tax revenue from wealthy Americans and spending cuts to help bring down deficits.
After agreeing in January to allow rates on top income earners to return to higher levels of the 1990s, Republican leaders say they oppose any further tax increases or other measures to raise more tax revenue.
Meanwhile, Carney told reporters to expect Obama to release his budget proposal during the week of April 8, which GOP critics quickly noted would be well after the House and Senate versions came out.
"This is the first time in 90 years that the president's budget will actually come up after both the House and Senate have voted," McConnell said. "I hope that's not a reflection of a lack of seriousness but it is beyond, beyond tardy."
By clearly staking out positions in the formal budgeting process, Obama and Congress appear intent on trying to avoid the crisis-driven brinksmanship of the past four years that deepened Washington's defining political divide.
However, the familiarly partisan nature of Ryan's plan unveiled Tuesday and the Democratic response raised doubts of any lessening of that divide, which the public blames for legislative dysfunction.
A CBS News poll last week showed more than 70% of respondents want both sides to compromise to end the impasse over taxes and spending that dominated Obama's first term.
During the past four years, House Republicans passed partisan budgets that Senate Democrats ignored, forcing the repeated extension of past spending plans.
Meanwhile, the president's budget proposals generated little support in Congress.
The upcoming negotiations are complicated by lingering fiscal issues from past showdowns.
Deep cuts to military and other discretionary spending took effect this month, and both sides were expected to try to soften their impact through a separate funding measure for the rest of the current fiscal year, which ends September 30.
Called a continuing resolution, it must pass by March 27 to prevent a partial government shutdown. The Republican-led House passed its version last week, and the Democratic-led Senate was expected to take up its own version as soon as Tuesday.
Congress also must authorize an increase in the federal borrowing limit this summer.
Obama still calls for a comprehensive deficit-reduction package that would overhaul the tax system, cut spending and reform popular entitlement programs.
He and fellow Democrats insist that such an approach, labeled the grand bargain, must include increased tax revenue from wealthy Americans to prevent the burden of austerity steps in spending and entitlement reforms from hitting the middle class, the elderly and other vulnerable demographics too hard.
"My goal is not to chase a balanced budget just for the sake of balance," Obama said in the ABC interview. "My goal is how do we grow the economy, put people back to work, and if we do that we are going to be bringing in more revenue."
"If we control spending and we have a smart entitlement package, then potentially what you have is balance — but it is not balance on the backs of the poor, the elderly, students who need student loans, families that have disabled kids. That is not the right way to balance our budget," he added.
Republicans led by their conservative base seek to shrink the size and cost of government, opposing any new tax revenue while pushing for spending cuts and lower tax rates that they say will spur more economic growth.
A comprehensive deficit-reduction deal appeared close during Obama's first term, but eventually fell apart over the deep ideological differences regarding taxes.
Such an agreement would reform the tax system to lower both personal and corporate rates while eliminating some loopholes and breaks. It also would reform Medicare and Medicaid and possibly Social Security to ensure their solvency.
The major sticking point of a comprehensive agreement will be taxes.
Obama and Democrats want to eliminate tax breaks and loopholes worth about $600 billion over 10 years as part of a broader $1.2 trillion deficit-reduction package that would include entitlement reforms.
Some Republicans have indicated support for ending such tax breaks as part of a broad deal. However, the fiscal-cliff agreement in January that resulted in higher tax rates on top income earners galvanized opposition by GOP leaders to further increases in tax revenue.
A sticking point in a possible compromise on taxes would be whether increased revenue realized through reforms, such as eliminating existing loopholes, go toward holding down rates or reducing the deficit.
Meanwhile, Republicans say Obama and Democrats must deliver on significant entitlement reforms.
"Democrats cannot be trusted to help fix our country's fiscal mess, if they cannot be trusted to balance the budget and create jobs," said a news release on Tuesday from the National Republican Congressional Committee. "The choice is clear: Democrats' perpetual deficits or Republicans' plan to balance the budget and spur economic growth."
One change Obama has proposed would tighten the adjustment for inflation of benefits such as Social Security, meaning annual increases for future recipients would grow at a slower pace.
Opponents of the reform, known as "chained CPI" in reference to the consumer price index it involves, argue it hurts vulnerable senior citizens and others who most need their benefits.
If achieved, a grand bargain would give Obama a major political victory and a boost in cementing his desired presidential legacy after the controversial health care and Wall Street reforms of his first term.
Republicans also would get credit from moderates and independents for a willingness to compromise, but conservatives could punish them with primary challenges in 2014 and beyond.
Another possible outcome is a limited agreement that would include some elements under discussion.
For example, a smaller agreement might end some tax breaks and loopholes while cutting Medicare costs paid providers, not beneficiaries, to achieve $500 billion or so in deficit reduction over 10 years.
Such a result, coupled with previous spending cuts and the January fiscal-cliff deal, would fail to reach the total $4 trillion in deficit reduction over the next decade that economists and political leaders have targeted as the minimum amount needed.
It also would allow both parties to simultaneously claim credit for making some progress after the past years of dysfunction while continuing to blame the other for preventing more.
A status quo outcome of no major deficit reduction steps would mean continued brinksmanship over each pending fiscal deadline, as well as further economic uncertainty that already has lowered the U.S. credit rating and slowed growth.
CNNMoney's Jeanne Sahadi and Rich Barbieri and CNN's Ted Barrett, Jim Acosta, Ashley Killough, Paul Steinhauser and Deirdre Walsh contributed to this report.