Washington (CNN) - Sen. Rand Paul on Sunday proposed an alternative way to avert a government shutdown, saying the two chambers of Congress should go to conference on the short-term spending bill at the center of the current stalemate.
"Why don't we have a conference committee on this? You could appoint one today. They could meet tomorrow and hash out the differences. That's the way it's supposed to work," he said on CBS's "Face the Nation."
Follow @politicalticker Follow @KilloughCNN
Conference committees are a common process Congress uses when both houses pass competing bills and they need to reconcile the differences.
Rep. Debbie Wasserman Schultz, chairwoman of the Democratic National Committee, said on CNN's "State of the Union" they "could absolutely" have a conference committee over an appropriations bill, but "we don't have conference committees over the CR." She was referring to continuing resolutions, another name for spending bills that fund the government for a short period of time until a full fiscal year budget can be passed.
And Senate Democratic Whip Dick Durbin argued Democrats have been trying "for more than six months to get the Senate Republicans to agree to a conference committee" on a full budget - but to no avail.
After a midnight vote, the House sent back to the Senate a bill on Sunday with two anti-Obamacare provisions: a yearlong delay to the federal health care law, and a repeal of its medical device tax.
Durbin said he's open to talking with Republicans about making changes to the health care law, but not at the risk of a government shutdown. "I'm willing to look at that, but not with a gun to my head," he said on "Face the Nation."
Asked if he expects a shutdown to happen, he said, "I'm afraid I do."
"I predict the Senate is going to reject this House overture that was sent to us last night," he added.
Meanwhile, Paul said he is also against a shutdown but doesn't think the president should get everything he wants on Obamacare. He supported the House version that came back to the Senate, because he said the chamber compromised and asked for a delay to the law, rather than proposing to defund it, as it did in the bill earlier this week.
But Senate Majority Leader Harry Reid has already pledged to reject the bill, and the president has issued a veto threat.
"We are the party that's willing to compromise," Paul said. "They're the party that says, 'No way, we're not touching Obamacare.'"
Other conservative Republicans also seemed supportive of the House's decision to ease the pedal and try to delay, not defund, the health care law.
Sens. Mike Lee and Ted Cruz both said Sunday they also approved of the House tactic, insisting it's the Democrats' turn to compromise.
"What the House of Representatives has done is a step removed from defunding. It's delaying it. Now that's the essence of a compromise," Cruz said on NBC's "Meet the Press." "For all of us who want to see it repealed, simply delaying it for American families on the same terms as is being done for big corporations, that's a compromise."
Watch State of the Union with Candy Crowley Sundays at 9am ET. For the latest from State of the Union click here.