The third-ranking House Republican said Sunday that if the Senate rejects the short-term spending bill the House just passed that takes aim at Obamacare, the House will promptly move to pass another bill that would change the health-care law.

"We will pass a bill, if the Senate does what you think they will do, that will keep the government open, that will reflect the House, that I believe the Senate can accept, that will have fundamental changes in Obamacare that can protect the economy," House Majority Whip Kevin McCarthy (R-Calif.) told Chris Wallace on "Fox News Sunday."

The government will partially shut down if lawmakers cannot strike a deal by the end of Monday. The House early Sunday passed a stopgap spending bill that would delay Obamacare by a year and repeal the medical device tax. The Democratic Senate has vowed to reject it. That will probably happen on Monday.

McCarthy refused to rule out passing a short-term continuing resolution that would keep the government running for days as negotiations continue.

Rep. Cathy McMorris Rodgers (R-Wash.), another top-ranking Republican, refused to say whether or not House Speaker John Boehner (R-Ohio) would allow a vote on a clean CR if the the Senate rejects the House's latest offering. "The Senate needs to act. It needs to act quickly," she said on CNN's "State of the Union."

The House also passed a bill to keep the military funded in the event of a shutdown. Sen. Tim Kaine (D-Va.) said that "in all likelihood" the Senate will pass that measure.