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 GrahamOvernight Defense: Top general talks Afghanistan, civilian casualties | Defense hawks slam short-term funding McCain and Graham: We won't back short-term government funding bill Members help package meals at Kraft Heinz charity event in DC MORE (R-S.C.) predicted on CBS’s “Face The Nation” that “I think we'll find consensus.” Senate Majority Harry ReidHarry ReidRepublican failure Senate about to enter 'nuclear option' death spiral Top GOP senator: 'Tragic mistake' if Democrats try to block Gorsuch 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 BoehnerPaul Ryan sells out conservatives with healthcare surrender Matt Schlapp: 5 lessons Trump, Ryan must learn from healthcare debate Nunes rebuffs calls for recusal 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 SchumerSenate seen as starting point for Trump’s infrastructure plan Dems wait for GOP olive branch after ObamaCare debacle How Obama's White House weaponized media against Trump 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 BoehnerPaul Ryan sells out conservatives with healthcare surrender Matt Schlapp: 5 lessons Trump, Ryan must learn from healthcare debate Nunes rebuffs calls for recusal 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 SessionsJeff SessionsFiorina calls for special prosecutor for Russia probe The Hill's 12:30 Report Dem rep: Sanctuary cities are actually ‘Fourth Amendment cities’ 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 CornynSenate Dems: Border wall is a budget 'poison pill' Senate braces for fallout over Supreme Court fight Former congressman indicted on conspiracy charges 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 RubioRepublicans giving Univision the cold shoulder: report Week ahead: Senate panel to vote on Trump's Labor pick Senators introduce new Iran sanctions 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.