But Sen. Tom Coburn, R-Okla. -- in a nod to similar comments by House Speaker John Boehner, R-Ohio, last week -- signaled the extension may need to include some cuts to spending in order to pass Congress.
Both the House and Senate are on their weeklong Presidents Day recess, which leaves about a week before the current stopgap spending measure expires on March 4. It's unclear whether that is enough time for Senate Democratic leaders, who have said they agree spending can be cut, and House Republicans leaders to strike a deal on the short-term extension.
Failure to put a spending package in place -- either a long-term deal or a short-term extension -- would lead to a shutdown of the federal government.
"I am willing to cut," McCaskill said on Fox News Sunday, but she stressed that she doesn't support many of the roughly $60 billion in reductions from current discretionary spending levels proposed in House GOP spending legislation approved Saturday morning.
She specifically cited proposed cuts to education spending and to border security efforts.
"I think we are serious about making cuts, I think we are serious about negotiating, I think we can sit down immediately and begin working on that," McCaskill said. But "we may need slightly to extend the current situation to work out a compromise that works for the American people."
Coburn, also on Fox, stressed that a government shutdown was not the desired result, but he said that cuts will have to be made sooner, possibly in the short-term extension, rather than later.
"I don't think we are" headed for a government shutdown, Coburn said. "Nobody wants that to happen."
"I think everybody realizes that we have to make some significant cuts," Coburn continued. But lawmakers "can't play the waiting game where people are saying, 'We don't want to agree to this now, give us a month.'... The fact is you'll get waited out and will still spend" at current levels.
"It's good for political rhetoric to talk about a government shutdown, but I think cooler heads" will prevail.
His comments come after Boehner said last week that he would not bring a short-term spending measure on the House floor.
House Budget Chairman Paul Ryan, R-Wis., agreed with Coburn and Boehner when he said on CBS's Face the Nation that the GOP wants cuts but no government shutdown.
"We are not looking for a government shutdown, but at the same time we are not looking at rubber-stamping these really high, elevated spending levels that Congress blew through the joint two years ago," Ryan said. "We don't want to accept these really high levels of spending while we negotiate how to continue funding the government."
He added "my guess is that we will probably have some short-term extensions, while we negotiate these things, with spending cuts."
Senate Democrats have seized on Boehner's comments and charged that his hard line would lead to a shutdown.
"I'm going to be optimistic that everyone behaves like adults here and we can sit down and get this worked out, but the person who has brought up a government shutdown was John Boehner and the House Republicans," McCaskill said.
"We all want cuts; he's the one that saying he won't even do a week or two days" extension of the stopgap at current levels, she said. "The bottom line is we all want cuts. We can find a compromise... without cutting the heart out of education spending, without cutting border security."
She added that Boehner's comments are an obstacle to finding common ground.
"If we don't want to make political points and if we are not posturing for the extreme elements of our party, we can all sit down and find those compromises," McCaskill said. "That is what Boehner ought to be emphasizing."
House Budget Committee ranking member Chris Van Hollen, D-Md., said of the government shutdown, "I hope [the GOP] won't push it to that."
He was also critical of the House-passed spending bill. He said that the measure would threaten the economic recovery.