Top lawmakers from both parties appear to be employing similar strategies in high-stakes spending talks: Impose maximum political damage to the other side without allowing negotiations to collapse.

Senior Democrats and Republicans on Sunday traded barbs about who is following and who is leading – but played down the prospect of a government shutdown as the sides race to reach a fiscal 2011 spending deal before the current stopgap resolution expires April 8.

Sen. Lindsey GrahamLindsey Olin GrahamCongress punts fight over Dreamers to March Pence tours Rio Grande between US and Mexico GOP looks for Plan B after failure of immigration measures MORE (R-S.C.) predicted on CBS’s “Face The Nation” that “I think we'll find consensus.” Senate Majority Harry ReidHarry Mason ReidWATCH: There is no Trump-Russia collusion and the media should stop pushing this The demise of debate in Congress ‘North by Northwest,’ the Carter Page remake MORE (D-Nev.), on the same show, called the glass “half full” and added “I think we can work this out.”

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But the apparent urge to avoid a shutdown comes amid a political messaging war in which Democrats hope to cast Republicans as beholden to extremists in their ranks, while Republicans are seeking to cast Democratic leaders as unwilling to confront fiscal challenges head-on.

House Speaker John BoehnerJohn Andrew BoehnerRestoring fiscal sanity requires bipartisan courage GOP congressman slams primary rival for Ryan donations Speculation swirls about Kevin McCarthy’s future MORE (R-Ohio), in his party’s Saturday address, said there’s no agreement but signaled that he wants to move to other matters, noting that Congress must “get moving and pass a final bill that resolves last year’s budget mess while making real spending cuts – so we can tackle the bigger challenges facing job creation.”

Sen. Chuck SchumerCharles (Chuck) Ellis SchumerDemocrats now attack internet rules they once embraced Schumer: Trump budget would ‘cripple’ gun background checks Schumer: Senate Republicans' silence 'deafening' on guns, Russia MORE (D-N.Y.), who heads the political messaging operation for Senate Democrats, and Reid both used appearances on the talk shows to highlight pressure being put on Republicans from the Tea Party movement, which Schumer noted is seeing its favorability number fall in recent polling.

Asked if BoehnerJohn Andrew BoehnerRestoring fiscal sanity requires bipartisan courage GOP congressman slams primary rival for Ryan donations Speculation swirls about Kevin McCarthy’s future MORE and veteran Republicans are afraid of the Tea Party, Reid replied, “The answer is yes.”

“The Tea Party is dictating a lot that goes on in the Republican leadership in the House. And they shouldn't. It shouldn't be that way,” said Reid, who attacked GOP efforts to cut social programs such as Head Start.

“That's the Democratic spin,” Sen. Jeff SessionsJefferson (Jeff) Beauregard SessionsUnder pressure, Trump shifts blame for Russia intrusion Overnight Tech: Judge blocks AT&T request for DOJ communications | Facebook VP apologizes for tweets about Mueller probe | Tech wants Treasury to fight EU tax proposal Overnight Regulation: Trump to take steps to ban bump stocks | Trump eases rules on insurance sold outside of ObamaCare | FCC to officially rescind net neutrality Thursday | Obama EPA chief: Reg rollback won't stand MORE (R-Ala.) said on ABC’s “This Week.” “The Democrats have no plan except the president's plan which makes the debt worse than the current trajectory we're on.”

Sen. John CornynJohn CornynLawmakers feel pressure on guns Kasich’s campaign website tones down gun language after Florida shooting Murphy: Trump’s support for background check bill shows gun politics ‘shifting rapidly’ MORE (R-Texas) said the Republicans, through the party's majority in the House, had already done their part in the budget process.

"I think it’s up to Harry Reid," Cornyn said. "I hope we can solve the problem because, frankly, people are looking for a little adult interaction and are interested in solutions to our debt and our deficit instead of games, and it looks like that’s what we’re getting."

The Republican refrain – in opposition to Democrats claiming that the Tea Party is in control – was that Senate Democrats were the party holding up a budget.

“This is a good opportunity to remind ourselves of why we're still debating the 2011 budget a third of the way in 2011's calendar year,” Sen. Marco RubioMarco Antonio RubioColbert: Students taking action on gun violence 'give me hope' Lawmakers feel pressure on guns Florida lawmaker's aide fired after claiming shooting survivors were 'actors' MORE (R-Fla.) said on “Fox News Sunday.” “And that's because the Democrats, when they control the House, the Senate and White House, did not offer or pass a budget. In fact, our Senate Democrat colleagues still have not.”

But Graham, speaking on CBS, predicted there will be a spending deal because conservative Democrats drive their party’s leaders there. “I think there are enough red-state Democrats who do not want to take this fight any further. They do want to be seen as reducing spending,” he said.

And Graham countered the claims that Republicans are acting only on behalf of a small group of ideologues.

“Our friends in the House, Speaker Boehner, who replaced Speaker Pelosi, is doing what the American people want in the last election: trying to reduce the size and scope of the government, which is a goal shared by the Tea Party,” Graham said.