M. Spencer Green/Associated Press

Reince Priebus, the chairman of the Republican National Committee, never misses a chance to accuse President Obama of being a terrible leader. So it was inevitable that he would pronounce Mr. Obama’s Rose Garden speech today about problems with the federal health insurance Web site a sign of a “fundamental breakdown in leadership.”

But some Republicans are actually getting weary of their party’s approach to the Affordable Care Act.

Jeb Bush, the former governor of Florida, continued his pre-Presidential campaign campaign by arguing that the G.O.P. made a huge mistake when it shut down the government in an attempt to dismantle the health law.



If they had shown some “self-restraint,” he said in an interview with ABC that was broadcast on Sunday, the government shutdown would not have eclipsed media coverage of problems with the site.

He also said that Republicans should try coming up with a reform plan of their own instead of just complaining about Mr. Obama’s ideas.

“I think the best way to repeal Obamacare is to have an alternative,” Mr. Bush said. “We never hear the alternative. We could do this in a much lower cost with improved quality based on our principles, free market principle. And two, show how Obamacare, flawed to its core, doesn’t work.”

Senator Tom Coburn, the Oklahoma Republican, offered a similar analysis. “The fight on Obamacare, or the Affordable Care Act, took us off message,” he said on NBC’s “Meet the Press” on Sunday. “The large percentage of American public knows that Washington wastes money. They just don’t have a clue of how bad it really is and so we lost the message there of what really needs to happen in Washington.”

(That, he said, is deficit reduction.)

Meanwhile, in Texas, the state government is actually urging residents to obtain health insurance coverage through A.C.A. exchanges, and is shutting down a state-run high-risk insurance program — because the A.C.A. has rendered it unnecessary.

Texans will have to do that through the technologically paralyzed federal Web site, however, because Gov. Rick Perry was one of those Republican governors who refused to set up a state insurance exchange for purely ideological reasons.