Less than 24 hours after the Senate passed legislation eliminating Members’ annual pay increases, the bill’s main proponents began efforts to shore up support in the House.

House leaders have been lukewarm on the prospect of bringing it to the floor, but Sens. David Vitter (R-La.) and Russ Feingold (D-Wis.) are hoping that Members can exert enough pressure to force the majority’s hand.

Vitter was successful in doing so in the Senate, where he forced a vote on an amendment to the omnibus that would have ended the automatic cost-of-living adjustments.

The amendment failed, but only after Majority Leader Harry Reid (D-Nev.) promised to present an identical stand-alone bill. That bill passed Tuesday.

Now, Rep. Jim Matheson (D-Utah) has introduced the same bill in the House.

On Wednesday, Feingold sent a letter to Speaker Nancy Pelosi (D-Calif.) asking her to follow Reid’s lead and bring the bill to the floor for debate. The automatic raise, he wrote, is an “outrageous perk— funded by taxpayers.

“As you know, Americans are justifiably outraged at the lavish bonuses that have been awarded to executives at firms now owned, in whole or in part, by US taxpayers,— he wrote. “If members of Congress believe that they deserve a bonus, they should be willing to offer legislation and have debates and votes in the open.—

Vitter, meanwhile, has begun reaching out to probable allies in the House, including Members who have supported similar legislation in the past, such as Rep. Harry Mitchell (D-Ariz.).

One senior Republican aide with knowledge of the efforts said that list could also include Republican Study Committee Chairman Tom Price (Ga.), as well as other caucus leaders who might be able to hold sway with large groups of Members.

Vitter also launched an online petition to put pressure on party leaders to end what he called in a statement “this outrageous, self-serving practice.—

Vitter’s spokesman, Joel DiGrado, said the Congressman is just beginning his efforts.

“Sen. Vitter is going to make a concerted effort to reach out to House Members and try to coordinate a way to continue to apply pressure on the Speaker and Majority Leader to make sure the issue sees a vote,— he said.

If the bill makes it to the floor, Members will probably pass it, if only because of the political stigma associated with voting against it.

In fact, the automatic pay raise is an issue that resurfaces every few years. Begun in 1989, the law automatically increases Members’ salary based on inflation. Most years, it’s 2 percent to 3 percent.

But every time the economy goes sour, Congress suspends its pay. Most recently, Members stuck an amendment in the omnibus to freeze their 2010 scheduled increase. They had received a $4,700 raise in January, bringing their annual salary to $174,000.

Getting rid of the automatic pay increase is a step further than the pay freeze, forcing Members to decide in an up-or-down vote whether they get a raise every year.

For two decades, House and Senate leaders have kept such a bill off the chambers’ floors, while the two parties have had an off-and-on agreement to keep the issue out of campaign politics.

But this could be the year that all falls apart. With unemployment skyrocketing and the recent outrage over AIG bonuses, pressure is high for Members to block their own automatic pay raises.

Still, Pelosi and House Majority Leader Steny Hoyer (D-Md.) have made it clear they don’t want to bring such legislation to the House floor.

Last week, Pelosi insisted Members “have an opportunity to vote on that each year,— referring to the annual procedural motion where Members vote on whether to have an up-or-down vote on the automatic increase.

Hoyer, who fixes the legislative calendar, has been more blunt.

“I’m not for it,— he said Tuesday, “so I’m not going to commit to bringing it to the floor.—

But Members who support the bill have some options.

Feingold is considering pushing for a discharge petition, where 218 House Members force a vote on a bill.

Republicans could also attach an amendment to a motion to recommit, putting Democrats in the uncomfortable situation of voting on whether to attach a pay raise amendment to another bill.

Minority Leader John Boehner (R-Ohio) hasn’t yet committed to pursuing such tactics, with his spokesman only confirming that he “supports the bill that was passed by the Senate.

“Beyond that, we will reserve all of our legislative options for the future,— spokesman Kevin Smith said.