House Speaker John Boehner and Majority Whip Kevin McCarty AP If, as expected, the Senate tables both House-passed amendments that chip away at Obamacare, House Republicans plan to move a new continuing resolution that alters the Affordable Care Act.

House Majority Whip Kevin McCarthy (R-Calif.) said on "Fox News Sunday" that leadership had a few options in store in the case of Senate rejection that would make changes to President Barack Obama's health care law.

Early Sunday morning along highly partisan lines, the House passed an amendment to delay Obamacare by one year and to repeal a new tax on medical devices. Both are likely to be rejected by the Senate and Majority Leader Harry Reid.

If that happens, McCarthy said the House will look to pass a bill that "will have fundamental changes into Obamacare that can protect the economy for America," he told host Chris Wallace.

McCarthy pledged that "we are not shutting the government down." But if the House adopts his plan going forward, there may not be enough time to avoid hitting the shutdown deadline. The federal government will partially shut down on Tuesday if the two chambers cannot come to agreement on the continuing resolution.

The Senate will not reconvene until Monday at 2 p.m. Shortly thereafter, it is expected to table both House-passed amendments, sending back a so-called "clean" continuing resolution to the House.

It's not clear what the House is looking to do, specifically, from here. McCarthy would only say that there are "a lot of items on the table."

One option that was discussed among leadership Saturday was the addition of language mirroring an amendment offered by Sen. David Vitter (R-La.). But this would face several problems, from the possible lack of conservative support to revolt from staffers who would be barred from receiving subsidies for federal health insurance under Obamacare.

If a government shutdown does result, McCarthy argued, Democrats and Obama should be to blame.

"We are not shutting the government down," he said on "Fox News Sunday."

"While the president was out playing golf, we were here until 1 a.m. We will pass a bill that reflects this House. … I think they’ll be additions that Democrats can support."