Congress so far has failed to finish any of the 12 regular spending bills to fund federal agency programs in the fiscal year starting on Oct. 1.

House of Representatives Speaker Kevin McCarthy will push an ambitious plan this week to win approval of four large bills, including military and homeland security funding, that he hopes would demonstrate enough progress to far-right Republicans to win their support for a stop-gap spending bill, known as a continuing resolution, or CR, as well.

Republican Representative Michael McCaul, a 19-year veteran of Congress who chairs the House Intelligence Committee, urged the group of party "holdouts" to stop blocking Republican-backed spending bills while at the same time "saying don't bring bipartisan bills to the floor."

"Republicans need to vote for Republican bills" to avert a shutdown, McCaul said on ABC's "This Week" broadcast.

But some of those "holdouts," who want deep spending cuts that go beyond a deal passed earlier this year, showed no sign of relenting.

"Continuing resolutions don't solve the problem. They just kick the can down the road," Republican Representative Tony Gonzalez told CBS News' "Face the Nation."

In June, President Joe Biden signed into law an increase in U.S. borrowing authority that he brokered with McCarthy, which also came with around $1.5 trillion in spending cuts over 10 years.

Ultra-right House Republicans want to go further with around $120 billion in additional cuts just for the new fiscal year, which could hit programs ranging from education and environmental protection to Internal Revenue Service enforcement and medical research.

Similarly, Republican Representative Tim Burchett told CNN's "State of the Union" that he has never voted for a temporary funding bill and won't this time around.

He warned that if McCarthy allows legislation to pass the House with Democratic support, "I would look strongly at" a move to strip McCarthy of his speakership.

"This dysfunctional Washington cannot continue," Burchett said, referring to the way Congress handles the federal budget, which is on a path to a $1.5 trillion deficit for the fiscal year that ends on Saturday.

Transportation Secretary Pete Buttigieg warned in an ABC interview that a government shutdown will require his agency to immediately suspend air traffic controller training courses at a time when air travel is "getting back to normal" following a high volume of flight delays and disruptions last year.

Aides to McCarthy were not immediately available for comment on whether negotiations over a CR were continuing on Sunday.

But he has been pushing for a 30-day bill to keep federal offices open, coupled with a strict border security plan that would basically suspend most immigration into the United States at a time of record numbers of people seeking asylum on the border with Mexico.

Even some of the Senate's most conservative Republicans on Sunday appealed to House counterparts to stop blocking a stop-gap bill.

"We would like for the House to begin that process of sending us a CR to keep the government open and functioning," Senator Marsha Blackburn told Fox Business News.

Appealing to those conservatives' eagerness for conducting investigations into Biden and some other top administration officials, Blackburn added: "If you shut down the government you can't continue that."

(Reporting by Richard Cowan and Sarah N. Lynch; Editing by Bill Berkrot)

By Richard Cowan and Sarah N. Lynch