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 GrahamCNN to air sexual harassment Town Hall featuring Gretchen Carlson, Anita Hill Trump wrestles with handling American enemy combatants Flake: Trump's call for DOJ to probe Democrats 'not normal' MORE (R-S.C.) predicted on CBS’s “Face The Nation” that “I think we'll find consensus.” Senate Majority Harry ReidHarry ReidTop Lobbyists 2017: Grass roots Boehner confronted Reid after criticism from Senate floor GOP in uncharted territory rolling back rules through resolutions 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 BoehnerThe two-party system is dying — let’s put it out of its misery One year later, neither party can get past last year's election White House strikes back at Bushes over legacy 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. Charles SchumerCharles (Chuck) Ellis SchumerTrump is right: The visa lotto has got to go Schumer predicts bipartisan support for passing DACA fix this year No room for amnesty in our government spending bill 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 John BoehnerJohn Andrew BoehnerThe two-party system is dying — let’s put it out of its misery One year later, neither party can get past last year's election White House strikes back at Bushes over legacy 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 SessionsCurtis wins Chaffetz's former Utah House seat Overnight Cybersecurity: What we learned from Carter Page's House Intel testimony | House to mark up foreign intel reform law | FBI can't access Texas shooter's phone | Sessions to testify at hearing amid Russia scrutiny FBI can’t unlock Texas shooter’s phone 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 CornynAfter Texas shooting, lawmakers question whether military has systemic reporting problem Overnight Defense: Lawmakers question military's lapse after Texas shooting | Trump asks North Korea to 'make a deal' | Senate panel approves Army pick Overnight Regulation: House passes bill to overturn joint-employer rule | Trump officials to allow work requirements for Medicaid | Lawmakers 'alarmed' by EPA's science board changes 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 RubioOvernight Cybersecurity: What we learned from Carter Page's House Intel testimony | House to mark up foreign intel reform law | FBI can't access Texas shooter's phone | Sessions to testify at hearing amid Russia scrutiny Cornyn: Senate GOP tax plan to be released Thursday This week: GOP seeks to advance tax overhaul 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.