WASHINGTON (AP) - Sign-up season for President Barack Obama's health care law is off to a stronger start this year. But it's not perfect, and Americans remain skeptical that the government's newest social program is right for the country.

As one major enrollment deadline loomed Monday, officials granted a last-minute extension for some consumers facing long telephone hold times at the federal call center. They were being asked to leave a number to get called back starting today.

Public attitudes toward Obama's signature law are only slightly less chilly than before the congressional midterm elections that saw Republicans, still clamoring for its repeal, win both chambers of Congress.

An Associated Press-GfK poll earlier this month found an uptick for the Affordable Care Act, with 29 percent saying they support it, compared with 25 percent in October. Opposition to "Obamacare" was stable at 41 percent, while the rest were on the fence.

In most states, midnight Monday, Pacific time, was the deadline for new customers to pick a health plan to take effect Jan. 1. It was also the deadline for current enrollees to make changes that could reduce premium increases before the new year.

Open enrollment actually runs for another two months, until Feb. 15. People enrolling by that date will get coverage starting March 1. Current customers can still make plan changes through Feb 15.

As recently as last week, administration officials were saying there was no plan to extend Monday's deadline. But late in the day, spokesman Aaron Albright said because of long wait times at the call center, some callers were being asked to leave a number. "We will call them back at a convenient time starting tomorrow, and if they select a plan, their coverage will still begin on Jan. 1," Albright said in a statement.

Despite the deadline jam, the administration seems to be on the way to reaching its self-imposed target of 9.1 million people enrolled for 2015.

Based on early numbers, it's looking like the majority of the 6.7 million current customers have opted to stay in their current plans and be automatically renewed on Jan. 1. Making sure that happens as smoothly as it has been advertised is the administration's next major challenge.

In Des Moines, Iowa, Cheryl James said she and two of her adult nieces helped each other and managed to sign up without too much trouble. James, who is studying early childhood education, found out she qualified for almost no-cost insurance under Iowa's Medicaid expansion, financed through the health care law.

"We are pretty satisfied with the coverage," said James, who's in her late 40s. "It took a couple of tries, but we weren't frustrated. It wasn't difficult."

Like Iowa, Tennessee has a Republican governor. On Monday it became the 28th state to accept the health care law's Medicaid expansion. Even as congressional Republicans are still vowing to overturn the law, 10 GOP governors have initiated expansions in their states.

As Monday's deadline for Jan. 1 coverage approached, HealthCare.gov and state health insurance websites saw a jump in traffic. Wait times at the federal call center stretched to 20 minutes and longer. The federal government is running the insurance markets in 37 states. Also known as exchanges, the markets offer subsidized private plans to people who don't have coverage on the job.

Health insurance companies can no longer turn people away because of health problems, but picking a plan still is daunting for many. Consumers also have to navigate the process of applying for or updating federal subsidies, which can be complex. Many returning customers are contending with premium increases generally in the mid-to-high single digits, but much more in some cases.