Topeka ? Speaker Mike O’Neal and other Republicans pledged support Thursday for a proposed rule that would require spending cuts to offset any new increases as the Kansas House prepares to begin its first significant budget debate.

The rule, which supporters call “pay as you go” or “paygo,” is similar to a measure Congress approved last year. It would prohibit members of the Kansas House, during debate by the entire chamber, from proposing amendments to appropriations bills adding spending to one part of the budget without coupling that with a cut in another part.

“We’ve got to have a balanced budget, and so if you’re going to be serious about wanting to add money, then you ought to be serious about finding a way to pay for it,” said O’Neal, a Hutchinson Republican.

But opponents are already lining up a possible constitutional challenge if the rule is approved. House Minority Leader Paul Davis, a Lawrence Democrat, said he is researching whether the proposed rule violates the state constitution by limiting legislators’ power to appropriate state funds. He wouldn’t rule out a court challenge.

“There is nothing that is more important that we do here than allocate expenditures, and the roughly 25,000 people that I represent deserve to have a vote on what that amount is going to be,” said Davis, who’s not an Appropriations Committee member. “The speaker has a majority of votes to do whatever he wants, and I don’t see why this is necessary.”

Congress operated with rules in the 1990s that said spending increases or tax cuts had to be offset so the federal deficit wouldn’t increase, but the rules became looser and members often found ways around them before enacting the 2010 version in a law that also raised the limit on the federal debt. Democrats frequently cited “paygo” principles in opposing tax cuts proposed by Republicans.

The Kansas House’s version of “paygo” is designed to limit spending. The state already can’t run a deficit, and legislators are already limited in what revenue-raising provisions they can slip into budget bills. Tax hikes, for example, must be approved separately.

Some House Republicans have wanted such a rule for several years but haven’t found enough support, even with a GOP majority. Last year’s elections left the Legislature more conservative, and the House’s 92-33 Republican majority includes 33 GOP freshmen, many sympathetic to the tea party movement’s focus on fiscal restraint.

The House expects to debate rules for the 2011 and 2012 legislative sessions by early next week and put them in place before debating a bill to trim spending from the current budget. The set of rules drafted by a House committee includes the new “paygo” requirement.

Davis said the rule would give too much power over spending issues to as few as a dozen House members — enough for a majority on the budget-writing Appropriations Committee. He said once the committee decides how much the state should spend overall, members won’t be able to revise the figure during debate.

The state faces a projected $550 million shortfall between anticipated revenues and current spending commitments for the fiscal year beginning July 1, although legislative researchers are preparing to revise the figure in light of better-than-expected tax collections in January.

Republican Gov. Sam Brownback wants to get started on closing the gap by cutting spending in the current budget and allowing the savings to roll over into the next fiscal year. But debating a bill without a “paygo” rule in place would allow the House to be less aggressive than its Appropriations Committee in reducing overall spending.

The Senate doesn’t have a “paygo” requirement, though Majority Leader Jay Emler, a Lindsborg Republican, said there’s an unwritten rule that members who propose to increase spending should propose a way to pay for it.

And while Brownback, a former U.S. senator, is staying out of the debate over the House rule, he told The Associated Press, “I think those have been useful tools federally.”

GOP leaders have complained for years about the House’s willingness to add money to spending bills, even when members acknowledge the state doesn’t have the revenues to cover it. And members of both parties have grumbled about “gotcha” amendments designed to generate recorded votes to use against them in campaigns.

O’Neal said the new rule would save time by eliminating frivolous or political amendments, and Appropriations Committee Chairman Marc Rhoades, a Newton Republican, called it “a no-brainer” because of the state’s budget problems.

Freshman Rep. Terri Lois Gregory, a Baldwin Republican, also favors the new rule.

“I think this will be much more transparent, and I think that we owe it to our constituents, that they see, ‘Where is this money going to come from?'” she said.