Then there are those taking what they call a pragmatic approach by accepting the law, if grudgingly, and moving on.

This group includes Governors Chris Christie of New Jersey and Scott Walker of Wisconsin, who says a shutdown would violate the public trust.

Walker said at a Republican rally in Michigan on Saturday: "The government we have should work, so that's why I don't believe we should shut the government down."

The Republican-controlled House of Representatives passed a short-term spending plan on Friday that would continue funding government operations through to mid-December while withholding money for implementing the health law.

Some Republican lawmakers also advocate holding back on increasing the nation's borrowing limit, which could result in a first-ever default, unless the law is brought down.

Obama used his weekly radio and internet address on Saturday to scold "a faction on the far right" of the Republican Party.

He said he would not allow anyone "to harm this country's reputation or threaten to inflict economic pain on millions of our own people, just to make an ideological point".

Even Senator Rand Paul of Kentucky, another tea party favourite, was sounding more like Bush by suggesting there was little Congress could do to stop Obamacare from taking effect.

Paul said while attending the Michigan rally that Republicans could force a vote in both houses of Congress, then negotiate changes to legislation in a joint conference committee. But, he added, time is running out.

"I'm acknowledging we probably can't defeat or get rid of Obamacare," he said. "But by starting with our position of not funding it may be we get to a position where we make it less bad."

Fewer than a quarter of Americans approve of the job Congress is doing, about the same as approve of Republicans in Congress, according to recent national polls.

Democrats poll slightly higher, and large majorities disapprove of the work of both.

Michigan Governor Rick Snyder said a shutdown would "reflect poorly on the national political culture."

But Bush was more pointed, saying Republicans would be guilty of overplaying their hand if they passed a spending measure that did not include money for the health care law.

Noting that Republicans control only the House of Representatives in Washington, or "one-half of one-third of the leverage" in the capital, Bush said there "needs to be an understanding of that, or, politically, it gets quite dicey" for the party.

Cruz said concerns that voters would blame Republicans for a shutdown are unfounded.

"If history is a guide, the fear of deep political repercussions - I don't think the data bears that out," he said.