Lawmakers vied for the political high ground Sunday, as they prepared to enter what could be the final stretch of this year's budget negotiations.

With Washington careening toward a Friday deadline to either come up with a plan or face a partial government shutdown, Democrats and Republicans continued to bicker over whether there is or is not a compromise on the table.

Aides to both parties confirmed to Fox News that policymakers are indeed working off a skeleton of a proposal that cuts $33 billion from last year's spending levels -- without such a starting figure, budget staff would be unable to write a bill. But lawmakers performed what amounts to a political dance in describing those negotiations, with Democrats sounding as if all that needs to be done is cross a few T's.

Senate Majority Leader Harry Reid, D-Nev., repeated the claim Sunday that the two sides have "agreed on a number."

Sen. Charles Schumer, D-N.Y., also said lawmakers are working off a proposal to cut $33 billion from last year's levels. "I'm quite optimistic," he said.

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House Speaker John Boehner, R-Ohio, though, has said several times this past week that there is no deal until all the details are worked out. After President Obama called Boehner and Reid over the weekend, Boehner spokesman Michael Steel said the speaker "reminded the president that there is no 'deal' or agreement on a final number, and he will continue to push for the largest possible spending cuts."

Boehner claims to be pushing for a package that more closely resembles the House-passed bill, which contained $61 billion in cuts.

Both sides are trying to protect themselves politically in case talks fall through. A failure to draft a bill for the rest of the year means they would have to either craft another unpopular stopgap bill or face a partial shutdown.

Right now, staffers are trying to whip up a budget proposal that achieves $33 billion in cuts. That number could rise, particularly if Democrats shoot down too many of the Republicans' policy riders -- which targeted organizations like Planned Parenthood for specific spending cuts.

Some GOP lawmakers are urging the party to hold its ground while others have indicated a willingness to back off the $61 billion figure.

Sen. John Cornyn, R-Texas, said Sunday he'd "like to cut more" but that it's up to Reid to take the next step.

Members of Congress nevertheless kept up the drumbeat of accusations, with the GOP accusing Senate Democrats of dropping the ball and Democrats accusing House Republicans of listening too much to the "extreme" Tea Party. Reid went so far as to call Republicans' House proposal "mean-spirited," saying it goes after "poor little children" by cutting funding to Head Start, an assistance program for low-income children.

Both parties tried to use the latest jobs report to bolster their arguments.

That report, released Friday, showed the unemployment rate dipping to 8.8 percent, with the economy adding 216,000 jobs -- nowhere near where the economy was before the recession, but a marked improvement over where it was just a few months ago.

Alabama Republican Sen. Jeff Sessions said the job growth could be imperiled by failing to deal with the national debt.

The debt "creates a threat of a crisis that could put us back into recession," Sessions said on ABC's This Week." "We have got to make changes now."

But Schumer, speaking alongside Sessions, said the job gains show why lawmakers can't cut the budget too aggressively.

"We have to deal with the deficit very seriously. But we also have to deal with the economy and job growth," Schumer said. "And we don't want to snuff that out."

The ongoing debate over the fiscal 2011 budget is just a prelude to the debate over the 2012 budget proposal. Rep. Paul Ryan, R-Wis., chairman of the House Budget Committee, told "Fox News Sunday" that the GOP proposal, set to be unveiled Tuesday, would cut more than $4 trillion over the next decade, through spending caps and changes to entitlement programs.

Democrats, in response, accused Republicans of protecting corporate interests at the expense of seniors, laying the groundwork for another bitter debate.

But Sen. Marco Rubio, R-Fla., suggested the course of the long-term struggle over the federal budget will be set now.

"What we do on the rest of this year's budget will be a strong indicator of how willing and how serious we are about dealing with our debt problem," he told "Fox News Sunday."

Rubio reiterated his pledge to vote against raising the debt ceiling unless it's "the last time we do it" and is accompanied by "meaningful reforms."

Cornyn, speaking on CNN's "State of the Union," made a similar pledge.

Sen. Mark Warner, D-Va., though, said, "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."

"You've got to believe cooler, saner heads will prevail on the debt limit as well," he said on the same program.

Fox News' Trish Turner contributed to this report.