Washington (CNN) -- President Barack Obama wrapped up three days of personal outreach on Capitol Hill, holding what both sides called a "great" meeting on Thursday with Senate Republicans who urged him to deliver the necessary Democratic support for making needed reforms to popular entitlement programs.
"He certainly understands that you can't fix the country without adjusting entitlements to fit the demographics of our country," said Senate GOP leader Mitch McConnell, usually a harsh critic of the president. "And we'll see where we go from here, but it was a great meeting."
For his part, Obama labeled the more than 90-minute meeting as a "great conversation" as he headed to a separate gathering with House Democrats opposed to significant changes to Medicare and Medicaid, which provide health care to senior citizens, the poor and the disabled.
After the second meeting, Obama said progress was made, and some House Democrats expressed willingness to discuss changes to entitlement programs as part of a broad agreement that would include GOP concessions on taxes.
The two meetings concluded a week of what reporters dubbed Obama's "charm offensive" -- a series of talks with legislators -- as Congress began debating budget proposals for 2014.
A formal budget process, with both chambers considering separate plans from each party that would be debated and negotiated in coming months, is considered the last opportunity this year to forge a compromise on reducing the nation's chronic federal deficits and debt.
Such an agreement proved unreachable in Obama's first term and the president emphasized during his meeting with Senate Republicans on Thursday that he sought bipartisan solutions to major issues after his re-election, according to participants.
"He mentioned there are some theories out there that he's trying to lure everyone into a trap, if you will, as a way to take back the House or whatever, and he assured us he's simply trying to get a budget deal done," said Sen. Jeff Flake, R-Arizona. "So as much as our base or others are convinced the president has nefarious motives, he challenged us to challenge them on that."
In addition, Obama told the GOP senators that "he's going to have to bring some people from his party along on entitlement reforms who don't want anything to happen, and he challenged us to do the same," Flake said.
Asked if any of the meeting could be labeled contentious, Flake answered "no."
The positive response, with none of the usual partisan rhetoric that has dominated political debate in Washington, signaled that both sides perceived a willingness in the other to tackle at least some of the tax and spending issues that have proven intractable in recent years.
"We need from him two things," said McConnell, R-Kentucky. "He needs to be directly involved, not -- as we used to say -- leading from behind, but directly involved. And his job is to deliver the members of his party."
In particular, he said, Obama must explain the need for entitlement reforms.
Obama's liberal base opposes any significant changes to entitlements, arguing senior citizens paid into the programs during their lives and deserve the benefits promised them such as health care coverage and Social Security checks.
"Only one person in the government has a big enough pulpit to explain that," McConnell said.
In the meeting with House Democrats, Obama discussed entitlement reforms including his offer to tighten the adjustment for inflation of benefits such as Social Security, meaning annual increases for future recipients would grow at a slower pace, according to participants.
Opponents of the reform, known as "chained CPI" in reference to the Consumer Price Index it involves, argue it hurts senior citizens and others who most need their benefits.
However, some House Democrats indicated after the meeting they were open to discussing such a change if Republicans showed they were open to increased tax revenue.
"We're not going to entertain any significant entitlement conversation until the Republicans meet us halfway with a revenue conversation," said Rep. G.K. Butterfield, D-North Carolina. "Those two conversations must be able to happen at the same time."
Rep. Nita Lowey, D-New York, said she opposed the chained CPI idea, but was willing to discuss it because Obama told the meeting there could be exceptions to protect "the most vulnerable."
Meanwhle, McConnell and other GOP senators said they agreed with Obama in their meeting on the need to overhaul the corporate tax system to lower rates in order to make American companies more competitive abroad.
However, House Speaker John Boehner offered a less optimistic view a day after Obama met with House Republicans, telling reporters that "this is going to take more than dinner dates and phone calls."
"The president's idea of compromise is just 'do it my way,' and that's not going to work," Boehner said in reference to the call by Obama and Democrats for increased tax revenue to be part of any compromise on deficit reduction.
Noting that Congress approved a return to higher tax rates of the 1990s on top income earners in January, Boehner said Obama "got his tax hikes" in that deal and "now it's time to cut spending."
White House spokesman Jay Carney said Obama was fully aware of the "enormous obstacles" to compromise.
He blamed what he called "an absolutist position" by Republicans such as Boehner in opposing the Democratic demand for deficit reduction to include both spending cuts and increased tax revenue.
Carney characterized such opponents as saying "no way, no how" to more revenue even though "the public ultimately supports that approach, even though there are voices in the Republican Party who believe that's the right approach to take."
"We'll see if there are enough members -- Republican members -- of the caucus of common sense to allow for progress to be made," he added.
Compromise is needed to prevent a recurrence of political showdowns like those from Obama's first term that contributed to a downgrade of the U.S. credit rating and sluggish economic recovery.
In an interview broadcast Wednesday on ABC, Obama warned such agreement may prove unattainable.
"Right now what I'm trying to do is create an atmosphere where Democrats and Republicans can go ahead and get together and try to get something done," he said of his so-called charm offensive that has included a dinner with GOP senators, lunch with House leaders and the meetings with both party caucuses in Congress. "But ultimately it may be that the differences are just too wide."
Last week, the president invited a dozen Republican senators to dinner and hosted lunch with the top members of the House Budget Committee to launch what reporters dubbed the charm offensive.
His outreach continued this week with visits to the Capitol on Tuesday, Wednesday and Thursday, concluded by his meeting with House Democrats after the talks with Senate Republicans.
Meanwhile, both the House and Senate budget committees began working this week on separate spending proposals for fiscal year 2014 that reflected the deep partisan divisions in Washington over tax and funding issues.
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.
After agreeing in January to allow the higher tax rates on top income earners, Republican leaders say they oppose any further steps to raise taxes.
Obama and Democrats say they want to protect Medicare, Medicaid and Social Security, and that comprehensive deficit reduction must include increased taxes on wealthy Americans to prevent the burden of austerity steps from shifting too much to the middle class, the elderly and other vulnerable demographics.
The Senate budget proposal for 2014 by Budget Committee Chairwoman Patty Murray, D-Washington, called for a mix of increased tax revenue and spending cuts to reduce deficits by about $1.9 trillion over 10 years.
It would increase revenue by about $975 billion by eliminating and curtailing tax breaks and loopholes for wealthy Americans and corporations. It would also cut spending by an estimated $975 billion: $493 billion in domestic spending; $240 billion in defense spending; and $242 billion in interest savings.
The proposal included a $100 billion economic stimulus package for road and bridge repairs, as well as worker training, that Murray said would be paid for by curtailing tax breaks for high-income households and corporations.
However, the Senate plan avoided significant changes to popular entitlement programs such as Medicare and Medicaid, which are major drivers of federal deficits.
Obama will introduce his own budget proposal next month, and the president and Democrats concede their approaches would not eliminate annual deficits, as sought by Republicans, but instead reduce them to what they say are manageable levels.
Republicans call such an approach inadequate, insisting that government has become too large and costly to ensure needed economic growth.
House Budget Committee Chairman Paul Ryan, R-Wisconsin, proposed a conservative spending plan for 2014 that he said would eliminate the annual deficit in a decade without raising taxes.
It 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 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.
His Medicare revision 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.
By clearly staking out positions in their budget proposals, Obama and Congress appear intent on trying to avoid the crisis-driven brinksmanship of the past four years.
However, the familiar, partisan nature of the budget plans illuminated the continuing political division that 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 brinksmanship over taxes and spending that dominated Obama's first term.
During the past four years, House Republicans pushed through 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 Democrat-led Senate took up its own version this week.
Congress also must authorize an increase in the federal borrowing limit this summer, and Republicans have made clear they intend to leverage that moment to try to extract concessions.
A comprehensive deficit-reduction deal appeared close during Obama's first term, but eventually fell apart over taxes.
CNN's Deirdre Walsh, Dana Bash, Alan Silverleib, Ted Barrett and CNNMoney's Jeanne Sahadi contributed to this report.