The US Capitol.
Washington CNN  — 

House Republican leaders are moving behind the scenes to get their conference behind a plan that would raise the debt ceiling for one year with a slew of cuts and revenue raisers, a move intended to strengthen their negotiating position with the White House in the high-stakes standoff.

The goal is to put a bill on the House floor as soon as May that could pass the narrowly divided chamber and send a clear signal to President Joe Biden that any legislation raising the debt ceiling must have strings attached, according to GOP sources involved in the talks.

There is no official estimate yet for the amount of cuts and revenue raisers Republicans are seeking, but one source said the goal is to find $3 trillion to $4 trillion worth of budget savings over 10 years.

Over the two-week recess, top House Republicans have been speaking with their rank-and-file members to find consensus on a plan that has been under development from the GOP’s so-called five families, representing the various ideological wings of the conference

Republicans are not yet unified on the emerging plan, with one source familiar with the talks saying some of the more conservative members have pushed for more measures – such as tougher border security provisions and a repeal of green energy tax credits – and some of the more moderate members have raised concerns over proposed changes to Medicaid.

But GOP lawmakers have called the talks productive and expect internal discussions over a Republican-led plan, which are continuing Sunday, will also intensify when lawmakers return to Washington this week after recess.

House Speaker Kevin McCarthy plans to set the tone over the GOP demands with a speech Monday in New York. The California Republican previewed his message during a Sunday call with his conference, a source familiar with the matter told CNN.

It is not yet clear when the country could potentially face its first-ever default if the debt ceiling isn’t raised, but it could happen as soon as this summer or as late as the fall – something that could have drastic economic ramifications. The White House and Senate Democrats have said that the debt ceiling should be approved without any conditions and have challenged Republicans to produce a plan if they won’t move on a clean increase.

Even if House Republicans can pass their own plan, it has no chance of passing the Democratic-led Senate. But House GOP leaders believe passing their own bill would force the White House to negotiate a package of spending cuts in exchange for raising the debt ceiling.

Among the provisions under consideration in the GOP plan are rolling back domestic discretionary spending to fiscal 2022 levels, something that would spare the Pentagon’s budget. Republicans are also looking to rescind funding for certain programs enacted to provide Covid-19 relief, and they want to impose new work requirements for Medicaid beneficiaries under the age of 60 and with no dependents.

Republicans are also considering an overhaul to the federal regulatory process by giving Congress new power to reject rules imposed by the administration. Plus, the GOP believes it can raise new revenue through provisions that would make it quicker to greenlight major energy projects. And they are weighing a 2% cut to federal spending when Congress passes a stop-gap resolution to keep the government funded.

One senior GOP source said the reception has been mostly positive so far.

“I think we can get there,” the source said.

This story has been updated with additional information.

CNN’s Lauren Fox contributed to this report.