The debate over paying for the recovery from Hurricane Katrina continued Tuesday as various factions within the House GOP floated ideas for spending offsets and jockeyed for position.

Majority Leader Tom DeLay (R-Texas) embraced the idea of finding spending offsets but declined to endorse any specific proposals, while the conservative Republican Study Committee met with GOP leaders to discuss their own plans and Republican moderates focused on strengthening oversight of the massive federal outlays that are already under way.

The RSC’s meeting with the leadership Tuesday came as some leaders had grown concerned that the conservative group’s high-profile push for spending offsets were making the party look bad.

In classic Washington, D.C., fashion, one leadership aide described the meeting as a “frank” discussion, during which the RSC lawmakers were told that the total costs for Katrina were still unclear and that it was a useless exercise to try to find offsets for more than the $62 billion Congress has already appropriated.

“We don’t have a $200 billion supplemental request from the president,” said the leadership aide, who noted that the meeting ended with a spirit of cooperation. “We need to take a hard look at the RSC’s list [of offsets]. … If we have the votes to pass them, we’ll do them.”

While the RSC’s hand would be strengthened if the group could attract some moderate lawmakers to its cause, such outreach appears unlikely in this case.

Though the RSC and the centrist Tuesday Group have been able to work together occasionally in the past, particularly on budget process reform, the two GOP factions are singing from different songbooks on Katrina.

“A lot of the things the RSC wants to do, to the moderates, are unrealistic,” said Rep. Mike Castle (R-Del.), a leading Tuesday Group member.

Specifically, Castle and other moderate Members and aides said they would be unlikely to support the RSC proposal to delay implementation of the Medicare prescription drug bill for a year.

“I think that’s more posturing than it is reality at this point,” Castle said of the idea.

Instead, the Tuesday Group is primarily focused on implementing stringent oversight over the money Congress appropriates for Katrina. Many moderate lawmakers were in Chicago this past weekend to attend a Republican Main Street Partnership retreat, and those Members agreed to endorse a proposal by Rep. Jim Kolbe (R-Ariz.) to create a special inspector general to scrutinize Katrina spending.

But while the RSC has been vocal in staking out ground on the offsets issue, the Tuesday Group has been relatively quiet about its plans.

“We don’t copy the RSC. We do our own thing,” said Rep. Mark Kirk (R-Ill.), the co-chairman of the Tuesday Group.

Kirk suggested that the main difference between the two groups was stylistic, with the Tuesday Group preferring to work behind the scenes.

“The difference between us and the RSC is a lot less press releases,” Kirk said. “I’m less interested in getting a lot of attention and more interested in getting the special IG.”

The RSC will hold a press conference today to unveil the list of specific offset ideas the group shared with leadership Tuesday. Yet even within that conservative faction, the possibility remains that not every member will support all of the proposed spending cuts.

In an e-mail sent Monday to all RSC press secretaries, the office of the group’s chairman, Rep. Mike Pence (R-Ind.), wrote: “We are coming up with a list of federal savings … and are NOT asking all those who come to the press conference to endorse all the savings, but ARE SEEKING about 10 Members to specifically take ownership over one offset idea and speak to that at the press conference.”

As the RSC trumpets its plan, DeLay has spent this week sharpening his own message about how to deal with the budgetary consequences of Katrina.

At his press briefing last week, DeLay sparked controversy by lauding the GOP’s record of fiscal discipline and declaring an “ongoing victory” against government waste.

Following an outcry from his fellow conservatives, DeLay sought to clarify his remarks Tuesday as a he faced a barrage of questions from reporters seeking specific details on how the billions of dollars spent on Katrina might be offset.

While conceding that he spoke “inartfully” last week, DeLay reiterated his praise for the party’s overall record of fiscal accomplishment, saying that “this Republican House has been focussed on fiscal responsibility and fiscal restraint” since the GOP took power in 1995.

And after saying last week that he was waiting for someone to bring him a list of realistic spending offsets, DeLay reiterated Tuesday his desire to find spending cuts, though he declined to address many specific ideas.

“There are programs all over the federal budget that are bloated or wasteful or inefficiently using the funds we provide them, and I’m very interested in identifying them,” DeLay said.

While DeLay agrees in principle with his fellow conservatives about the importance of finding offsets, the Majority Leader was dismissive of the idea to delay the Medicare bill by a year.

“The president has already spoken on that, and it’s a non-starter,” DeLay said. Arguing that the Medicare bill was actually designed to save money in the long run anyway, DeLay said that “postponing a reform that is going to implement fiscal restraint doesn’t make a whole lot of sense.”

He was less clear in his views on another potential spending fix: reopening the highway bill to remove Member earmarks.

“It’s still an option, and we’re going to look at that [and] many others,” DeLay said, though he later emphasized the economic importance of the highway bill and political difficulties that would be associated with revisiting it.

After Minority Leader Nancy Pelosi (D-Calif.) said that she would be willing to forgo her highway bill earmarks to help pay for Katrina, DeLay was asked if he would do the same.

“I don’t know about that,” DeLay said. “I would take a look at it. My earmarks are pretty important to building an economy in that region.”

DeLay also criticized the idea of putting off extending President Bush’s tax cuts and said that they remained on the agenda, saying that not extending the cuts would be the equivalent of raising taxes.

“Katrina tax hikes are not about Katrina; they’re about tax hikes, and they are not an option,” he said.