Washington - Congress returns to work this week with no plan to reverse across-the-board spending cuts that took effect late Friday - but with hope on both sides of the aisle to avert an end-of-month showdown that could result in a government shutdown.

The House will vote on Thursday on a spending measure that would keep the government running after its current funding mechanism elapses on March 27.

It would provide funding through the end of the fiscal year on Sept. 30, allowing new flexibility to the Pentagon to manage the $40 billion hit the military took Friday but otherwise lock in lower spending levels that reflect the so-called sequester.

House Speaker John Boehner told "Meet the Press" that he discussed the need to avoid a possible shutdown with President Barack Obama during a meeting on Friday between the president and congressional leaders. The interview was filmed after that meeting and aired Sunday morning.

"The president this morning agreed that we should not have any talk of a government shutdown," Boehner said in the interview. "So I'm hopeful that the House and Senate will be able to work through this."

Following Boehner on "Meet the Press," Gene Sperling, the chairman of Obama's National Economic Council, agreed that it appeared likely the two sides could avoid threatening a shutdown.

That would mean the sequester would be here to stay through the remainder of the year. But Sperling insisted Obama will work to undo its cuts in coming months as part of a broader discussion about continued deficit reduction.

"We would still be committed to trying to find Republicans and Democrats that will work on a bipartisan compromise to eliminate, get rid of the sequester," he said.

Assuming the two sides agree to government spending for the latter half of the year soon, Washington's new major fiscal battle will probably come over the summer, when the nation once again bumps up against the debt ceiling.

Sperling said he believed the pain of the across-the-board spending reductions will make itself felt over the next few months and could cause Republicans to rethink their opposition to new tax revenue as part of debt deal - the crux of the difference that separates the two parties on fiscal issues.

"Our hope is that as more Republicans start to see this pain in their own districts that they will choose bipartisan compromise over this absolutist position," he said.

Sperling insisted that Obama remains open to the kind of deal last discussed between Boehner and Obama in December - in which Democrats would trade cuts to entitlements in exchange for closing tax loopholes and ending deductions, resulting in higher tax revenue.

Sperling said Obama spent part of Saturday making phone calls to rank-and-file senators in both parties who had expressed interest in that kind of "grand bargain," a potential first step to reviving the idea before Washington's next major budget clash.

The calls came after also Obama met at the White House last week with Sen. Lindsey Graham, R-S.C., and Sen. John McCain, R-Ariz.

Graham and Sen. Kelly Ayotte, R-N.H., both indicated Sunday they might have some interest in weighing a deal that would address debt through both reforms to mandatory entitlement programs and higher tax revenue.

"We don't need to raise taxes to fund the government," Graham said on CBS "Face the Nation. "We need to raise taxes to get our nation out of debt."

At a leadership level, Boehner and Senate Minority Leader Mitch McConnell, R-Ky., offered no indication Sunday that they had interest in budging on taxes.

Boehner said Republicans were done raising taxes, after agreeing to the "fiscal cliff" deal at the start of January that raised more than $600 billion in higher taxes. Any new revenue gained from closing tax loopholes, he said, should now be put into lowering tax rates.

"The president got $650 billion of higher taxes on the American people on January the 1st," Boehner said. "How much more does he want? When is the president going to address the spending side of this?"

And McConnell said he doubted calls from Obama to Republican senators would result in any deal that would replace even part of the sequester - originally agreed to in the 2011 bill that raised the debt ceiling - with higher taxes.

"So far, I haven't heard a single Senate Republican say they're willing to raise one dime in taxes in order to avoid a spending reduction commitment that we made on a bipartisan basis just a year and a half ago," McConnell said on CNN's "State of the Union."