WASHINGTON — Lawmakers from both major political parties Sunday expressed concern over the botched rollout of the new federal health insurance website, 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 the issues were symptomatic of larger problems with the law and that many of the disadvantages of the program are becoming glaringly apparent now that people are starting to be able to see the quality and cost of the coverage available under the law.

Sens. Joe Manchin, D-W.Va., and Jeanne Shaheen, D-N.H., took to the Sunday 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 for a bill delaying the so-called “individual mandate” for a year. Shaheen proposed extending the open enrollment period beyond its current end date of March 31 to account for all the people who have not been able to buy coverage thus far because of problems with the online shopping site, HealthCare.gov.

“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 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 enroll in coverage. With a month of the open enrollment period nearly over, it is only fair to extend that period, she said.

The Obama administration has so far dismissed proposals to extend any deadlines. On Friday, officials said they would 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 Health and Human Services Secretary Kathleen Sebelius to resign. On ABC’s “This Week,” Manchin said he has faith in her ability to lead the implementation of the law.

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

Meanwhile, people logging on to the new federal health insurance website Sunday encountered a new home page — one that does not feature the smiling brunette whose happy disposition stuck a discordant note for people unable to access the site.

The woman’s picture became so closely associated with the site that a number of journalists tried unsuccessfully to track her down.

The satirical publication the Onion ran a digitally altered picture of her looking worried, with the headline “People In Healthcare.gov Stock Photos Now Visibly Panicking.”

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

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