Friday was to be the deadline for states to declare their intentions. But Ms. Sebelius said Thursday night that she was extending the deadline to Dec. 14. In any event, she must decide by Jan. 1 whether states are able to run their own exchanges.

Americans are supposed to be able to start shopping for insurance through exchanges in October 2013. By January 2014, most Americans will be required to have health insurance under the law.

Obama administration officials said they would be ready to run the federal exchanges, but they have not provided any information about their plans or their progress.

Gov. Rick Scott of Florida, a Republican, asked Friday for a meeting with Ms. Sebelius to discuss plans for an exchange. He said he was still analyzing his options, but had not seen evidence that an exchange would lower health costs for Floridians.

Gov. Nathan Deal of Georgia, a Republican, said his state would not establish an exchange. He expressed concern about what he described as “the one-size-fits-all approach and high federal burden imposed on states.”

Other Republican governors, including Jan Brewer of Arizona, C. L. Otter of Idaho, Terry E. Branstad of Iowa, Chris Christie of New Jersey, Tom Corbett of Pennsylvania and Bill Haslam of Tennessee, said they would use the extra time to seek more answers from Washington and feedback from constituents.

In a letter to Ms. Sebelius, Mr. Branstad said his state wanted to create its own exchange, but needed much more information. He included a list of 50 questions and said that unless they were answered, Iowa might have no choice but to opt for a federal exchange.