WASHINGTON – Republican members of Congress on Sunday offered glimpses of rifts within their party after the government shutdown, suggesting that raw feelings might hobble progress on other pressing issues.

The leader of the conservative Republican opposition to the national health care law, which triggered the government shutdown, freshman Texas Sen. Ted Cruz remained defiant. Cruz said he would keep focusing on health care in the coming months, despite calls from the White House and members of both parties of Congress to take up such issues as immigration reform.

Cruz didn't rule out another push for a shutdown in January, when continued funding for the government will once again require congressional authorization. "I will continue to do anything I can to stop the train wreck that is Obamacare," Cruz said on ABC's "This Week." "What I intend to do is continue standing with the American people to work to stop Obamacare, because it isn't working, it's costing people's jobs, and it's taking away their health care."

He interpreted the bottom-of-the-barrel poll ratings for Congress that came out last week as a sign that Americans wanted Congress to work harder to dismantle Obamacare, rather than as a repudiation of its priorities. He sharply criticized his fellow Senate Republicans for agreeing to end the shutdown.

"I think the House Republicans marched out on principle to say we're listening to the people who are hurting because of Obamacare." And I wish that Senate Republicans had come in like the cavalry to support them," Cruz said on CNN's "State of the Union." "Instead, they made a decision not just to not support the House Republicans, but to come in like an air force and divebomb them."

Other, more senior GOP senators agreed on scrapping the health care law. But they took issue with shutting down the government again in 2014 as a negotiating ploy. Senate Minority Leader Mitch ­McConnell, R-Ky., said the GOP would do "everything possible" to repeal the Affordable Care Act but said that did not include another shutdown.

Senate Minority Leader Sen. Mitch McConnell, R-Ky., is followed by reporters after agreeing to the framework of a deal to avoid default and reopen the government on Capitol Hill on Wednesday, Oct. 16, 2013 in Washington. The partial government shutdown is in its third week and less than two days before the Treasury Department says it will be unable to borrow and will rely on a cash cushion to pay the country's bills. (AP Photo/Carolyn Kaster)

"A number of us were saying back in July that this strategy … would not work, and of course, it didn't. So there'll not be another government shutdown, you can count on that," McConnell said on CBS's "Face the Nation."

McConnell declined to criticize Cruz, whose popularity with the GOP's conservative base has amplified his clout despite his recent arrival on the national stage. But other GOP senators such as Lindsey Graham of South Carolina were more pointed about the effect of Cruz's approach.

"After this debacle called 'the shutdown' … our brand name's at the lowest ever," Graham said on "Face the Nation." "Obamacare actually got a bump in polling, and we got in the way of a disastrous rollout."

Graham added: "The shutdown should be in our rearview mirror as Republicans, 'Don't do this again, Ted.' "