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 GrahamGraham: Trump will 'end North Korea’s threat to the American homeland' in his first term Sunday shows preview: Lawmakers weigh in after Texas school shooting Kim Jong Un surprises with savvy power plays MORE (R-S.C.) predicted on CBS’s “Face The Nation” that “I think we'll find consensus.” Senate Majority Harry ReidHarry Mason ReidMcConnell not yet ready to change rules for Trump nominees The Hill's Morning Report — Sponsored by CVS Health — Trump’s love-hate relationship with the Senate Trump to press GOP on changing Senate rules 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 BoehnerGOP revolts multiply against retiring Ryan Can Jim Jordan become top House Republican? Tensions on immigration erupt in the House GOP 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 SchumerSchumer: GOP efforts to identify FBI informant 'close to crossing a legal line' Patients deserve the 'right to try' How the embassy move widens the partisan divide over Israel 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 BoehnerGOP revolts multiply against retiring Ryan Can Jim Jordan become top House Republican? Tensions on immigration erupt in the House GOP 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 SessionsStopping Robert Mueller to protect us all Chris Christie compares Mueller investigation to 'Bridgegate' probe Oakland mayor fires back at Trump: ‘It’s my duty to protect my residents’ 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 CornynOvernight Finance: House panel to take up bill toughening review of foreign deals | Trump acknowledges Cohen payment on disclosure form | Officials set for new round of China trade talks Groups urge Senate panel to reject Trump's pick for Louisiana-based appeals court House panel will consider bill to boost foreign investment review powers next week 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 RubioCongress — when considering women’s health, don’t forget about lung cancer Anti-Maduro Venezuelans not unlike anti-Castro Cubans of yore Tax reform postmortem reveals lethal dose of crony capitalism 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.