no longer features these photos of smiling people, which struck a discordant note among users who had trouble with the site. (Andrew Harrer/Bloomberg)

Lawmakers from both major political parties expressed concern Sunday over the botched rollout of the federal health insurance Web site, with two Senate Democrats saying the problems are serious enough to justify delays to key provisions of the president’s health-care law.

Republicans, meanwhile, said that the issues are symptomatic of larger problems with the law and that many of the program’s disadvantages are becoming glaringly apparent now that people can begin to see the quality and cost of the coverage available.

Their comments came on another problematic day for the Web site, The insurance application part of the site was down for hours Sunday because of an outage at the Verizon data center that hosts the site.

“Today, [Verizon] had a network failure that is impacting a number of their clients, including,” Joanne Peters, a spokeswoman for the Department of Health and Human Services, said in a statement late Sunday. “Secretary [Kathleen] Sebelius spoke with the CEO of Verizon this afternoon to discuss the situation and they committed to fixing the problem as soon as possible.”

Earlier in the day, Democratic Sens. Joe Manchin III (W.Va.) and Jeanne Shaheen (N.H.) took to the talk shows to press for legislation that they said would give people more time to comply with a rule requiring most Americans to carry health insurance starting next year or face a fine.

Manchin advocated a bill delaying the “individual mandate” for a year. Shaheen proposed extending the open-enrollment period beyond its current end date of March 31 to account for the people who have not been able to buy coverage because of problems with

“My goal is to fix the Affordable Care Act to make sure those people can get that access to health care,” Shaheen said on CBS’s “Face the Nation.”

She said the rollout of the online marketplace has been a “disaster” because so many people have been thwarted by technological glitches as they try to view plan options and prices and buy coverage. With a month of open enrollment nearly over, it is only fair to extend that period, she said.

The Obama administration has dismissed proposals to extend any deadlines. On Friday, officials said they will fix the site by the end of November, giving people four months to buy coverage before they incur a penalty of as much as 1 percent of their income.

Insurers object to any delays in the mandate or penalty, partly because they set their prices for next year under the assumption that large numbers of young and healthy people, who are cheap to insure, would be compelled by the law to join their patient pools.

Neither Democrat echoed some Republicans’ calls for Sebelius to resign. On ABC’s “This Week,” Manchin said he has faith in her ability to lead the implementation of the law.

Shaheen sidestepped the question, saying the focus should be on fixing the Web site. “There’s going to be plenty of time to place blame on who is responsible,” she said.

Meanwhile, people logging on to the site Sunday encountered a new home page — one that did not feature the brunette whose happy smile struck a discordant note for people unable to access the site.

The picture became so closely associated with the site that a number of journalists tried unsuccessfully to track down the woman. The satirical publication the Onion ran a digitally altered picture of her looking worried, with the headline “People In Stock Photos Now Visibly Panicking.”

Gone, too, are the cheery pair on the page where users choose their state.

In their place are four new logos highlighting the ways consumers can apply for insurance coverage. Each links to a different option: the Web site, a paper application, a phone line and in-person helpers.

“ is a dynamic website,” Peters, the spokeswoman, said in a statement. “As with all websites, we try to make meaningful enhancements and improvements that will help users understand key information, while maintaining the overall familiar design and navigation elements that are working well.”

Several Republicans said the site’s problems are minor compared with larger issues with the program that are coming to light.

“The president made promises that this was going to be cheaper than your cellphone bill, easier to use than Amazon and you can keep your doctor,” Sen. John Barrasso (Wyo.) told host George Stephanopoulos on “This Week.” “People all across the country, George, are seeing that’s just not true.”

Last week, Kaiser Health News reported that insurers from Pennsylvania to Florida have sent notices to hundreds of thousands of people with private plans that their coverage is being terminated at year’s end. Blue Cross Blue Shield of Florida, for example, sent cancellation notices to 300,000 people.

The reason is that starting Jan. 1, most private insurance plans must cover 10 basic benefits, including maternity and pediatric dental care. Many plans currently sold on the individual market do not cover those benefits, and they are being discontinued.

On NBC’s “Meet the Press,” however, Florida Blue Cross Blue Shield chief executive Patrick J. Geraghty pushed back against the characterization that the plans are being “canceled.”

He said people are being told that they can’t keep their current plans but that they have new options that in some cases are better. For many people, he said, costs may go down because of government subsidies available to low- and middle-income customers on the marketplaces, also known as exchanges.

“We’re not cutting people — we’re transitioning these people,” he said. “What we’ve been doing is informing people that their plan doesn’t meet the test of the essential health benefits. Therefore, they have a choice of many options we make available through the exchange, and in fact, with subsidy, many people will be getting better plans at a lesser cost.”

Geraghty acknowledged, however, that some people’s costs will go up.

A March study commissioned by California’s health insurance exchange estimated that Californians who already buy coverage on the individual market but make too much to qualify for subsidies could see their premiums rise 30 percent because of the health-care law. The income cutoff for subsidies nationally is 400 percent of the federal poverty level, or about $94,200 for a family of four in 2013 dollars.

Gerald Kominski, director of the UCLA Center for Health Policy Research, said the tone of many of the termination letters received by plan-holders has apparently not been particularly reassuring. On call-in shows and in other venues where he hears from people whose plans are being terminated, he said, the news is being greeted with panic.

Some consumer advocates worry that the termination letters could be a back-door way for insurers to dump high-cost patients onto the online marketplaces.

Republicans say the letters also prove that the president was wrong when he said people who like their insurance can keep it under the health-care law, a refrain he has repeated at town hall meetings and in interviews.

Sarah Kliff contributed to this report.