Washington (CNN) - The top Democrat in the House is pushing back against calls to extend open enrollment in the new health care exchanges because of the massive technical problems plaguing HealthCare.gov.
"I don't support that," House Minority Leader Nancy Pelosi said Wednesday morning, just hours after Sen. Jeanne Shaheen of New Hampshire appeared to be the first Democrat in Congress to join a growing number of her Republican colleagues in suggesting the deadline be pushed back.
The current law stipulates that enrollment in the insurance exchanges set up by the Affordable Care Act ends on March 31, 2014. Those who are uninsured after that point face fines by the Internal Revenue Service.
"As website glitches persist, we are losing valuable time to educate and enroll people in insurance plans," Shaheen wrote in a letter to President Barack Obama. "I also fear that people that have tried, and failed, to enroll online may become frustrated and not return to the website to try again at a later date... Allowing extra time for consumers is critically important so they have the opportunity to become familiar with the website, survey their options and enroll."
When asked by CNN Senior Congressional Producer Deirdre Walsh, Pelosi said she disagreed with Shaheen, adding that "I think we should fix what we have. Move forward with the deadline we have, respectful of what her (Shaheen's) experience may be, of her suggestion, but not supportive of it."
Pelosi also told reporters on Capitol Hill that she didn't hear any members who took part in a closed door meeting of House Democrats and officials implementing the health care exchanges earlier Wednesday suggest that they wanted to push back the deadline.
But one senior House Democrat who spoke with CNN following the meeting didn't rule it out.
"I'm not prepared to say that now. We're going to have to find out," said longtime Rep. John Dingell of Michigan, a healthcare reform patriarch, when asked about pushing back the enrollment deadline or removing the fine.
Shaheen faces re-election next year in a purple state but early polling indicates she's far ahead of her possible GOP challengers. Regardless of her push to extend the deadline, Shaheen does not appear to be a turncoat in the war over Obamacare. The Senator's letter to the President offers high praise of - and some patient frustration with - the law.
Democratic Sen. Mark Pryor of Arkansas also supports pushing back the deadline.
"The senator has seen the letter and supports the effort to extend the enrollment deadline," Michael Teague, Pryor's communications director, told CNN Wednesday afternoon.
Pryor, like Shaheen, is also up for re-election next year. He faces a tough bid for another term in office in a red state and is being challenged by GOP Rep. Tom Cotton.
CNN's Conor Finnegan and Kevin Bohn contributed to this report