"Look, we're not looking for a government shutdown. But at the same time, we're also not looking at rubber-stamping these really high elevated spending levels that Congress blew through the joint two years ago," House Budget Committee Chairman Paul Ryan, R-Wis., said on CBS's "Face The Nation."
"My guess is we will probably have some short-term extensions while we negotiate these things with spending cuts," he said.
Lawmakers face a March 4 budget deadline, when a temporary governmentwide funding bill runs out. If no compromise is reached by then, the government could be forced to shut down.
Congress is currently on a weeklong Presidents' Day recess, so lawmakers will return with just four days left to agree on a temporary extension of the stopgap measure now financing the government.
The last time the government shut down was in late 1995 and early 1996, during a conflict between Democratic President Bill Clinton and the Republican-controlled Congress over funding for Medicare, education, the environment and public health.
Washington put non-essential government workers on furlough and suspended non-essential services Nov. 14-19, 1995, and Dec. 16, 1995-Jan. 6, 1996.
In the current standoff, Senate Republicans said they would agree to a temporary spending measure only if it included funding cuts.
"I won't support a (continuing resolution to authorize funding for departments until a new budgets is approved) unless it has some spending cuts," Senate Budge Committee member Lindsey Graham, R-S.C., told NBC's "Meet the Press."
U.S. Sen. Charles Schumer, D-N.Y., accused Republicans of using a government shutdown possibility as negotiation leverage.
"Many Republicans have said a shutdown is a good thing," Schumer said on CNN's "State of the Union." "So one thinks that they want to use the shutdown to get their way."
The Republican-controlled House voted 235-189 along partisan lines Saturday to cut $61 billion from current spending through Sept. 30.
The bill, which U.S. President Barack Obama threatened to veto, would ban funds for Obama's healthcare overhaul and for Planned Parenthood, which provides abortions. It also would scrap "net neutrality" Internet rules and block regulations on greenhouse gases and for-profit colleges.
It would be the biggest one-shot cut in discretionary spending in history, House Appropriations Committee records indicated.