Then there are those taking what they call a pragmatic approach by accepting the law, if grudgingly, and moving on. This group includes Govs. Chris Christie of New Jersey and Scott Walker of Wisconsin, who says a shutdown would violate the public trust.
"The government we have should work, so that's why I don't believe we should shut the government down," Walker told reporters after speaking at a Republican conference in Michigan on Saturday
The Republican-controlled House of Representatives passed a short-term spending plan Friday that would continue funding government operations through 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 Saturday to scold "a faction on the far right" of the Republican Party, and 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 Sen. Rand Paul of Kentucky, another tea party favorite, 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 conference 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 told reporters. "But by starting with our position of not funding it maybe we get to a position where we make it less bad."
Less than one-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 Gov. Rick Snyder, hosting a state Republican conference where Walker and two other 2016 prospects, Louisiana Gov. Bobby Jindal and Paul, planned to speak Saturday, said a shutdown "reflects poorly on the national political culture."
Jindal said this week, "I do think the party needs to be more than the party of 'no.'"
Bush was more pointed. He said Republicans would be guilty of overplaying their hand if they passed a spending measure that did not include money for the healthcare 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 bear that out," he said.
Republican lawmakers and Democratic President Bill Clinton failed to agree on spending in 1995, which resulted in two partial government shutdowns.
Clinton was re-elected the following year, but Cruz noted that Republicans held the majorities in both chambers of Congress in 1996 and 1998, and collaborated with Clinton on spending cuts and other changes that preceded economic expansion.