The Republican Study Committee, the most influential bloc of House of Representatives conservatives, on Monday unveiled its "Back to Basics" budget as an amendment that would replace Ryan's plan in a House floor vote this week.
The study committee's version includes $7.4 trillion in spending cuts compared with Ryan's proposed $5.1 trillion in cuts.
With only a scant chance of passage, the plan would give the most conservative House members, especially those backed by the Tea Party movement, some political cover with a chance to vote for both Ryan's plan and the more drastic RSC version.
The RSC is promoting "the same yes-yes strategy that we've employed in the past - yes on Ryan and yes on the RSC budget," said Stephen Bell, a spokesman for Republican Representative Steve Scalise, who chairs the RSC.
The RSC budget would eliminate deficits by 2018 compared with 2024 in Ryan's plan, partly by making deeper cuts to domestic programs.
Both budgets would change Medicare from a fee-for-service health care program for the elderly into a system that gives seniors a subsidy to help them buy coverage from Medicare or private insurers. Democrats say that approach would end the promise of guaranteed medical coverage that the current fee-for-service program provides.
But the RSC's version would start these changes sooner, for those turning 65 in 2019, compared with 2024 under the plan from Ryan, the House Budget Committee chairman.
House Republican leaders have expressed confidence that Ryan's budget will pass, despite complaints from Tea Party groups that it would increase discretionary spending levels for fiscal 2015 to stay in line with a short-term budget deal struck late last year.
While some conservatives may dislike the slight increase in discretionary spending, Republican Representative Tom Cole said Ryan's plan would offer the long-term savings on big social programs that they favor.
"If you've voted for it in the past, I would argue the safe thing is to stay consistent, not undercut yourself by not voting for what is essentially the same thing," Cole told Reuters.
House Democrats in this week's budget vote also will get a chance to vote for their ideal budget document, one that envisions higher spending across a range of programs from education to infrastructure, along with higher deficits than those proposed in President Barack Obama's budget requests.
The Democratic plan has no chance of passage because Republicans control the House 233-199, but the vote will feed into the party's campaign message of promoting policies to narrow the gap between rich and poor.
"Where Republicans in Congress gut funding that would boost the economy and help our nation succeed in the 21st century economy, we invest in our kids' education, infrastructure, and life-saving research," said Representative Chris Van Hollen, the document's author and the top House Budget Committee Democrat.
The House Democrats' budget, like Obama's, would close some tax breaks and boost revenues by about $8 trillion over 10 years compared with Ryan's plan. It would not achieve a balance and would run deficits as high as $753 billion in 2021, versus deficits of $504 billion for Obama's and $191 billion for Ryan's plan that same year.