But in the 36 mostly Republican states that left the operation of their exchanges to the federal government, consumer interest Tuesday was high, while Democrats and advocacy groups took the lead in promoting the latest provision of the law.
"I'm thrilled that the United States is finally catching up with some of the other countries in the world that provide health care," said Houston resident Priscilla McAfee, who planned to use an exchange to buy a policy.
McAfee, who said she now has a COBRA policy after losing her job, is among an estimated 7 million Americans that federal officials say could obtain policies through the exchanges in its first year. Several hundred thousand of those live in Texas, which has the highest proportion of uninsured residents of any state.
McAfee's governor, Republican Rick Perry, has been among the most vocal critics of the law. "I'm very grateful for the timing ... at a time that my need is so great," she said Tuesday.
The federal exchanges, which market policies from private insurers, opened Tuesday despite the partial government shutdown that began the same day because of congressional budget gridlock rooted in Republicans' continued opposition to the law they deride as "Obamacare."
Obama administration officials said 2.8 million users visited the healthcare.gov website during the first 15 hours after the exchanges opened. It was enough to slow the server and keep some consumers from completing enrollment. But several of them said they are still eager to learn more, particularly about tax credits that will help pay for their premiums.
McAfee said she expects her cost, once she qualifies for the income-base credits, to be about half the $500 she pays each month in her current coverage that expires Dec. 31.
Oi Thompson of Utah attended a health insurance fair in Salt Lake City. She said she understands about half of what is happening under the overhaul, but plans to wait a week before enrolling.
"If this plan works like we understand, it will be easy for us to get the insurance," she said.
Danny Copeland, a 58-year-old retired pipefitter from Muncie, Ind., said premium prices concern him, but he's pleased the law bars insurers from denying him coverage because he has diabetes. Copeland said he was unable to get through to actually buy a policy. "I understand it," he said. "This is the first bug. So there's not much you can do about it today."
Federal officials cast the glitches as a success, because it confirms the demand for new coverage.
"With any new product launch, there are going to be glitches, and we are going to fix them," said Marilyn Tavenner, administrator of the Centers for Medicare & Medicaid Services that manages heatlhcare.gov. "We added capacity, and we made adjustments to the system."
Tavenner also noted that Tuesday was just the first day of a six-month enrollment period, though consumers must buy policies by Dec. 15 for coverage to begin Jan. 1, 2014.
A few Republicans took the new glitches as an opportunity to again hammer the law itself.
"Our job is to get the information out there. The feds' job is to make it work. Unfortunately, it's not working," said South Carolina Gov. Nikki Haley, explaining that her office and her state's Medicaid agency fielded calls from residents struggling to use the federal website. "We're going to continue doing what we can," Haley said, "but this is continuing to be the mess we thought it would be."
That's more than what some Republican governors offered.
A spokesman for Georgia Gov. Nathan Deal dismissed the sweeping law as "a federal issue" and said his boss had no plans to discuss it.
State workers in several other GOP-run states were ordered to refer all questions from residents to federal offices. In Oklahoma, state employees were instructed to tell residents they are "not trained or certified to answer questions about the Federal Insurance Marketplace."
Many hospitals, health clinics and local community groups have filled the void using federal grants to pay "navigators" who are trained to help residents use the new marketplace. But even those federally paid helpers have faced obstacles.
In Texas, Perry ordered that navigators in his state train for an additional 40 hours beyond the 20 hours they already receive from Tavenner's agency. Tennessee Gov. Bill Haslam's Commerce Department imposed background checks on the navigators.
Florida's health department ordered county health departments to ban navigators from their property. Wisconsin and Indiana charged training fees for the navigators and volunteers.
Several government councils in Texas are no longer participating in the navigator program, according to a local United Way office that got $5.8 million to pay the workers. One attributed the decision to political pressure.
"There's a lot of strong feelings about this program in Austin — the legislative level, in the governor's office," said John Buckner, executive director of the Coastal Bend Council of Governments. "It seems like with all the issues going on right now, it might be best not to get involved with something that's not being very accepted by the political arena."
A handful of Republican states quietly made moves to help residents use the exchanges, even as their governors lambasted it publicly.
Like in South Carolina, the state insurance office in Louisiana has staff to answer questions. State officials in Wisconsin sent letters to about 92,000 people expected to lose Medicaid government insurance at the end of the year, directing them to the exchanges.
In Michigan, Republican Gov. Rick Snyder's administration created an online premium calculator and information site even after GOP lawmakers rebuffed the governor's call for the state to run its own exchange. The state's insurance agency also plans to host more than 50 events at local libraries across the state between now and the March end of enrollment.
Follow Barrow on Twitter @BillBarrowAP
Associated Press reporters contributing to this story included Seanna Adcox in Columbia, S.C.; Scott Bauer in Madison, Wisc.; Emery Dalesio in Raleigh, N.C.; David Eggert in Lansing, Mich.; Ramit Plushnick-Masti in Houston; Michelle L. Price in Salt Lake City; Tom LoBianco in Indianapolis; Erik Schelzig in Nashville, Tenn.; and Paul J. Weber in Austin, Texas.
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