Washington (CNN) -- Top senators said Sunday that they believe Congress will reach a deal to avoid a government shutdown this week, but there was little consensus on two larger budget battles looming in coming months.
Negotiations on federal spending for the rest of the current fiscal year, which ends September 30, have agreed on a target figure for a compromise on cuts. Now the question is whether they can work out exactly what programs should get axed.
Democratic Sen. Mark Warner of Virginia told CNN's "State of the Union" that he thinks a compromise will get worked out before the current measure authorizing government spending expires April 8.
"What kind of message do we send to this world if we are saying, we've agreed on a top line budget number, in terms of what we're going to cut this year, but then we're going to have these extraneous factors come in that have nothing to do with budget .. and that causes a shutdown?" Warner asked.
Republican Sen. Lindsey Graham of South Carolina told the CBS program "Face the Nation" that "I think we'll find consensus," while fellow Republican Sen. Jeff Sessions of Alabama and Democratic Sen. Charles Schumer of New York both expressed confidence for a deal on the ABC program "This Week."
So far, the two parties have agreed to $10 billion in cuts in temporary spending measures that have kept the government running, and now are considering more than $20 billion in additional cuts for the remainder of fiscal 2011.
The Republican-controlled House passed a bill calling for $61 billion in cuts, while Senate Democrats call that too much and are trying to work out a compromise at around half that figure.
Senate Majority Leader Harry Reid, D-Nevada, said on the CBS program that one problem in the talks is Republican negotiators feared a backlash from the conservative Tea Party movement if they meet Democrats halfway on a budget deal.
"The Republican leadership in the House has to make a decision on whether to do the right thing for the country or the right thing for the tea party," Reid said on CBS.
Due to a surge in conservative support driven by the Tea Party movement, Republicans won control of the House last November and reduced the Democratic majority in the Senate.
Tea Party activists already have criticized House Speaker John Boehner, R-Ohio, for signaling possible agreement on smaller cuts than called for in the bill passed by the House but rejected by the Senate.
In addition, conservatives are pressuring Republican leaders to include so-called "policy riders" in the spending measure that would strip government funding for programs such as Planned Parenthood.
However, Reid noted that a CNN poll last week showed the Tea Party movement was losing popularity among the general populace.
"The tea party is dictating a lot of what's going on in the Republican leadership now," Reid said on CBS, adding: "It shouldn't be that way."
Sessions acknowledged that the Tea Party movement may not "understand all the realities of Washington politics," but on the substance of the issues -- the need to reduce the size of government and bring down spending -- "they are right fundamentally," he told ABC.
Even with an agreement this week, Congress faces grueling negotiations soon on more substantive budget issues.
The United States will reach its legal borrowing limit of $14.29 trillion later this month or in May, requiring an increase of the federal debt ceiling.
Some Republicans say they will oppose raising the debt ceiling unless there are accompanying reforms intended to address long-term spending and national debt issues.
"That's the price that's going to have to be paid, systemic reforms, in order to get Republican support for raising the debt ceiling, otherwise I think you are going to see Democrats having to do that all by themselves," Republican Sen. John Cornyn of Texas said on CNN.
Another Republican, Tea Party favorite Sen. Marco Rubio of Florida, said he also would oppose increasing the debt limit unless it is accompanied by "meaningful reforms that put us on a path towards fiscal sanity."
"If all we do is go in there in three, four weeks or in a couple of months and extend the debt limit again and do nothing else, the world's going to look at us and say America and its political leadership is not serious about dealing with this incredible issue and the fact that their government continues to spend money it doesn't have," Rubio said on "Fox News Sunday."
Democrats questioned the rationale for anyone to oppose raising the debt ceiling, saying such a move would amount to a default on paying some debt with dire economic consequences.
"It just frightens the heck out of me that anyone responsible would say, let's go ahead and light the fuse that might create the next economic meltdown," Warner said.
At the same time, talks will escalate on a budget for the next fiscal year, with Democrats and Republicans both calling for a comprehensive approach that addresses long-term deficit issues.
Despite proclaiming similar goals, the two sides appear far apart on specifics. Both sides call for tax reform, but Republicans oppose increased revenue from higher taxes while Democrats want to end Bush-era tax cuts for wealthy Americans.
The two parties say military spending and entitlement programs such as Medicare, Medicaid and Social Security -- which together claim the bulk of federal spending -- must be targeted, but they differ on exactly what to include.
House Budget Chairman Rep. Paul Ryan said Sunday that his Republican budget proposal for 2012 will include dramatic changes to Medicare, Medicaid and other political lightning rods.
The plan, to be released Tuesday, calls for a controversial overhaul of Medicare, the health care program for seniors, and would impose deep cuts in Medicaid, which provides health benefits to low-income Americans, Ryan told "Fox News Sunday."
Starting 10 years from now, in 2021, elderly Americans would receive government help in paying health insurance premiums instead of enrolling in the government-run Medicare program, Ryan said.
The plan is modeled after one Ryan proposed last year with Alice Rivlin, budget director under President Bill Clinton. The Ryan-Rivlin plan said the amount of assistance would be calculated in part by taking the average federal cost per Medicare enrollee.
On Medicaid, Ryan's proposal would provide states with block grants to cover the costs of health coverage for the poor. Sources said the plan would cut Medicaid spending by up to $1 trillion, though Ryan provided no specific figure on Sunday.
Ryan, R-Wisconsin, said his plan would bring "well over" $2 trillion in savings in coming years, and he criticized President Barack Obama for offering a 2012 budget proposal that contained no reforms of entitlement programs.
In addition, Ryan said, his proposal would change the tax code to lower rates but eliminate some exemptions and broaden the tax base. Asked for specifics, he instead repeated the Republican mantra that the nation needed to cut spending to balance the budget and reduce deficits, not raise taxes.
Warner questioned Ryan's plan.
"My understanding is he will do all of these things and not look at defense spending, not look at major tax reform that would raise revenues," Warner said on CNN, adding: "I'll give anybody the benefit of the doubt until I get a chance to look at the details, but I think the only way you're really going to get there is you have to put everything there, including defense spending and tax reform as part of the overall package."
CNN's Dana Bash, Deirdre Walsh and Gabriella Schwarz contributed to this story.