The breakdown among Republicans was 81-17 in favor of state control, while independents lined up 65-28 for states taking the lead. Democrats were almost evenly divided, with a slim majority favoring state control.
There are several potential benefits to a state operating its own exchange, experts say.
The biggest advantage may be that states would be more closely involved in coordinating between the exchanges and Medicaid programs. Because many people are going to be going back and forth between Medicaid and private coverage in the exchanges, states would probably be better served by a hands-on role.
States can also decide whether to allow open access to all insurers, or work only with a panel of pre-screened companies that meet certain requirements.
Also, the exchanges will offer coverage to people buying in the individual and small business markets, areas that states have traditionally regulated. Without a state-run exchange, states could be dealing their own regulators out of the equation, as Mississippi's insurance commissioner Chaney noted.
When the legislation was being considered in Congress, Democrats in the House wanted to have a national exchange administered by the federal government. But they lost the argument with their centrist Democratic counterparts in the Senate, who wanted state exchanges in order to preserve a state role.
Despite signs of movement toward going along with implementation of the overhaul, some major Republican-led states are holding fast. In Texas, the election results did not change any of the opposition to expanding Medicaid or to setting up insurance exchanges. The same holds for Louisiana, South Carolina, Missouri, Kansas and others.
"Adding more people to an already sinking ship with money that is either being borrowed from China or coming out of taxpayers' pockets is bad policy and bad for Texans," said Catherine Frazier, spokeswoman for Gov. Rick Perry. Twenty-seven percent of that state's residents are uninsured, the largest percentage for any state.
Many Republican state officials complain that the Obama administration simply hasn't given them enough information. Indeed, several major regulations affecting the exchanges have yet to be released. But that doesn't seem to have stopped states that made an early decision to proceed. Republican governors requested the extension granted Thursday.
Virginia, a Republican-led state that voted for Obama on Nov. 6 and also elected a Democratic U.S. senator, is among those defaulting to Washington. But a spokesman for Gov. Bob McDonnell said things may change.
"This is not a final decision," said Jeff Caldwell. "The fact is, states still need far more information before any final decisions can be made on behalf of Virginia's taxpayers."
Associated Press writers Gary Fineout and Kelli Kennedy in Florida, Grant Schulte in Nebraska, Ann Sanner in Ohio, Jeff Amy and Emily Wagster Pettus in Mississippi, Barry Massey in New Mexico and Chris Tomlinson in Texas contributed to this report.