House Republican leaders have begun courting moderate Democrats on several key fiscal issues, including a deal to avoid a government shutdown at the end of next week, risking an angry backlash from conservative constituents but aware that consensus within their own ranks seems out of reach.

The basic outline on a budget deal would involve more than $30 billion in cuts for the 2011 spending package, well short of the $61 billion initially demanded by freshman Republicans and other conservatives, according to senior aides in both parties.

Such an agreement probably would be acceptable to Senate leaders and President Obama as long as the House didn’t impose funding restrictions on certain social and regulatory programs supported by Democrats, Senate and administration aides said.

After 54 conservatives voted against a stopgap budget measure two weeks ago that passed with significant Democratic support, House Majority Whip Kevin McCarthy (R-Calif.) met with a conservative bloc of Democrats to discuss potential common ground on the budget and other pressing fiscal issues.

Asked Wednesday morning about meeting, McCarthy acknowledged that it took place but suggested its main purpose was to look at longer term budget issues, particularly entitlement reform.

“The Blue Dogs had asked to meet with me when I got elected Majority Whip,” McCarthy said. “I sat down and had a meeting with them after the [March 15 vote], so it wasn’t about that. What I want to talk about with the Blue Dogs is if they’re serious about saving these entitlements ... and the budget going forward.”

On Tuesday, Rep. Heath Shuler (N.C.) suggested McCarthy had requested the meeting. Shuler, a centrist Democratic leader, said McCarthy did not specifically ask for Blue Dog votes on any legislation, saying that the conversation was taking place at “10,000 feet” and that the Republican was “feeling us out.”

The Democrats left the meeting knowing that they could provide the decisive votes, Shuler said, a role they are willing to play. “We’re looking for ways to help,” he said. “We’re for real. We’re not here for the politics.”

The fact that Republican leaders have initiated talks with some Democrats shows some division within House Republicans just two months after taking over the House. Speaker John A. Boehner’s leadership team recognizes that legislation that meets with approval from his most conservative flank — what Democrats call the “perfectionist caucus” — would be dead on arrival in the Democratic-controlled Senate.

At the same time, conservatives have become increasingly unhappy with recent spending proposals, saying they wouldn’t cut deep enough.

A deal with Democrats could avoid a government shutdown and point the way for future compromises. But it also could come at a steep price for Republican leaders who risk the ire of some conservatives, including those who are attending a tea party rally Thursday on Capitol Hill to demand the deepest spending cuts possible.

What many leaders in Washington may consider a sensible compromise to ensure that the government keeps running is just the sort of dealmaking that many Republican voters view as unprincipled capitulation. Some tea party groups have promised to target any Republicans they think are not conservative enough on fiscal issues.

However, if such a bipartisan coalition emerged, the House could have a path for not only approving a spending plan for the remaining six months of the fiscal year, but for a vote later this spring on whether to increase the federal debt limit. That normally routine action is in peril this year because some Republicans have said they are unwilling to raise the ceiling without significant concessions from Democrats on spending.

Tug of war

The two sides continued sparring this week over the parameters of a budget deal.

House Majority Leader Eric Cantor (R-Va.) announced Wednesday morning that House Republicans would introduce a symbolic measure that would essentially be a re-vote on the funding measure already passed by the House last month, in an attempt to pressure the Senate to act.

Republicans are blaming Senate Democrats for not passing a bill to be matched against the $61 billion in cuts approved in the House. Democrats reject the House legislation as a starting point for negotiations, noting that it was turned down in the Senate and arguing that they should build up from $10 billion in savings that were already agreed upon.

The rhetoric has been heated enough that Boehner and Senate Majority Leader Harry M. Reid (D-Nev.) both issued the same threat, refusing to “negotiate with ourselves” while in fact neither side would negotiate at all. No new face-to-face talks have been scheduled, and the two sides have until April 8 to approve a spending plan or face a government shutdown.

On top of the $10 billion in savings, Democrats are willing to offer an additional $20 billion in spending cuts.

But they said they will not do so until they are assured that it would get them close to an agreement.

House Republicans want to use their bill as a starting point because it also includes provisions that limit funding for some social and regulatory issues.

“It’s just not cutting spending. There are a number of limitations that passed on the floor of the House” that must be addressed, Boehner said.

Those provisions have created a large hurdle for securing a final deal. Republican aides have said the provisions and the overall cost cutting are linked: The fewer that are attached to the bill, the bigger the cuts Republicans will seek.

Even so, if the provisions remain and spending cuts are on the lower side, Boehner could lose support from freshman lawmakers in his party.

But without the provisions, some socially conservative longtime lawmakers may balk at the deal.

The Blue Dogs’ role

With 241 Republicans, GOP leaders can afford to lose 23 GOP votes before needing Democratic help. That’s why McCarthy reached out to leaders of the Blue Dog Coalition, a group of centrist Democrats — such as Shuler — from conservative-leaning districts.

The blueprint for this potential coalition was a March 15 vote to extend government funding for three weeks.

The vote easily passed with 271 votes, but only because 186 Republicans were joined by 85 Democrats.

House Minority Whip Steny H. Hoyer (D-Md.) said it is too soon to tell whether that vote “was a pattern or an anomaly.” Viewed as an ally of the Blue Dogs and other moderate Democrats, Hoyer read quotes to reporters from some of the most conservative House Republicans suggesting that a government shutdown would be preferable to a compromise.

He dismissed any chance of Republicans reaching a final deal that did not include Democratic support. “John Boehner can’t get something done without us,” Hoyer said Tuesday.

As tenuous as the potential coalition is, Shuler said his group of Democrats hopes that a bipartisan deal can be reached on this year’s spending bill so that it can serve as a framework for larger issues, including next year’s budget and other reforms.

“The real debate has to begin,” he said. “I think we can be a bridge-builder between the two parties.”