President Barack Obama called yesterday for Congress to craft a short-term plan to prevent across-the-board Pentagon cuts from starting next month, spurring exasperated responses from Republicans wary of any tax increases.

Obama did not offer a specific proposal to stop “sequestration.” That’s the $1.2 trillion decade-long cut to defense and non-defense spending that is unpopular in Washington but slated to start in March because Democrats and Republicans disagree about how to stop it. At a White House press conference Obama called on lawmakers to present an alternate plan with added revenues and spending cuts that will delay the start of sequestration, so lawmakers can work on a broader budget package.

“If Congress…can’t get a bigger package done by the time the sequester is scheduled to go into effect, then I believe that they should at least pass a smaller package of spending cuts and tax reforms that would delay the economically damaging effects of the sequester for a few more months until Congress finds a way to replace these cuts with a smarter solution,” Obama said during brief remarks to reporters.

He argued there “is no reason that the jobs of thousands of Americans who work in national security or education or clean energy, not to mention the growth of the entire economy, should be put in jeopardy just because folks in Washington couldn’t come together to eliminate a few special-interest tax loopholes or government programs that we agree need some reform.”

Obama’s comments come as key lawmakers including House Budget Committee Chairman Paul Ryan (R-Wis.), who believes Republicans should not agree to any more tax-rate increases, have been saying sequestration will kick in. Still, at the same time, Senate Democrats are working on a new budget plan that does away with sequestration through steps including tax reforms Obama favors. And Republicans in both chambers have offered multiple ways to stop the sequestration cuts, via reductions to social programs Democrats favor and reductions to the federal workforce.

Obama referred to ongoing work in Congress on “a budget that would permanently replace the sequester.”

“At the very least, we should give them the chance to come up with this budget instead of making indiscriminate cuts now that will cost us jobs and significantly slow down our recovery,” he said. He spoke in favor of a separate, longer-term deal that would stop sequestration through a “balanced approach of spending cuts and entitlement reform and tax reform,” such as what he offered House Speaker John Boehner (R-Ohio) last year.

Boehner, though, issued a statement slamming Obama’s support for a short-term solution before the president even announced it yesterday afternoon. The Republican leader rejected any increased taxes and noted the GOP-led House has already passed legislation, that Senate Democrats ignored, to replace sequestration with reductions to other funding such as health care and food stamps.

“We believe there is a better way to reduce the deficit, but Americans do not support sacrificing real spending cuts for more tax hikes,” Boehner said, continuing to place the blame for sequestration on Obama. “The president’s sequester should be replaced with spending cuts and reforms that will start us on the path to balancing the budget in 10 years.”

Defense-minded Republicans said yesterday they are happy Obama has joined in the sequestration debate but signaled a wariness to revenue schemes, such as increased taxes, he would support.

“We welcome President Obama to the table, perhaps better late than never,” House Armed Services Committee Chairman Howard “Buck” McKeon (R-Calif.) and Senate Armed Services Committee (SASC) Ranking Member James Inhofe (R-Okla.) said in a joint statement.

“We are, however, concerned that his proposal will include the same mix of tax increases and defense cuts that Democrats have advocated for in the past,” they said, calling that approach “neither responsible nor balanced.”

SASC members John McCain (R-Ariz.), Lindsey Graham (R-S.C.) and Kelly Ayotte (R-N.H.) also slammed Obama’s late entry to the sequestration debate, saying in a joint statement: “We appreciate that the President now wants to come to the negotiating table and we will examine his proposal closely.”

The three hawkish Republicans said they will reintroduce legislation to offset the first year of the sequestration cuts to the Pentagon–which would see a $500 billion decade-long reduction–by freezing the size of the federal workforce. McKeon backed similar federal-workforce legislation in the House last year, though the idea did not advance in either chamber of Congress.

Senate Democrats, meanwhile, met for a two-day retreat yesterday in Annapolis, Md., where they were expected to hear from Senate Appropriations Committee Chairwoman Barbara Mikulski (D-Md.) about preventing sequestration through alternate cuts and new revenues.

House Democrats, for their part, lauded Obama’s comments yesterday. House Minority Leader Nancy Pelosi (D-Calif.) said Obama’s “ideas echo the proposal offered by congressional Democrats to replace the sequester with responsible spending cuts and measures to close tax loopholes for the largest oil and gas companies.”

“House Democrats stand ready to get the job done,” she said in a statement. “We must act to put people to work, preserve investments in our middle class and in our national defense, and bring down the deficit.”

Her comments came as the Republican-led House began debating the Require a PLAN Act. The GOP bills says if Obama’s fiscal year 2014 spending proposal does not result in a balanced budget he must submit a plan before April identifying when he will balance the nation’s finances. Republicans on the House Rules Committee on Monday night blocked an amendment from House Budget Committee Ranking Member Chris Van Hollen (D-Md.) that called for eliminating sequestration through other spending cuts and revenues including tax increases on wealthier Americans and the eliminations of tax benefits to oil and gas companies.