Plenty of Republicans have piled on disapproval about the problems with the health insurance exchange website, but now many of President Obama's own allies are joining the chorus of criticism with some Democrats even calling on the president to delay the law.

In a speech on the House floor Wednesday, Rep. John Barrow, a Blue Dog Democrat from Georgia, called on the president to delay implementation of the law's individual mandate, which is set to be enforced Jan. 1.

"This isn't about pointing fingers. This is about providing some relief to the folks we represent who are facing serious uncertainty because they're being forced to buy something that's not ready," Barrow said. "I urge my colleagues and the administration to delay the individual mandate. It's not only the right thing to do, it's the only practical thing to do."

Some Democratic lawmakers are still praising the president's signature healthcare plan, but they've turned their frustration toward the botched rollout and are venting about how it could hurt their constituents' ability to access healthcare.

Sen. Jeanne Shaheen, D-N.H., asked President Obama to extend the open enrollment period beyond the current date of March 31, 2014, until the website glitches are fixed, arguing that the problems have dampened people's ability to sign up for the exchanges.

"As website glitches persist, we are losing valuable time to educate and enroll people in insurance plans. 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," Shaheen wrote in a letter to the president Tuesday. "Allowing extra time for consumers is critically important so they have the opportunity to become familiar with the website, survey their options and enroll."

Sen. Mark Pryor, D-Ark., who like Shaheen is up for re-election in 2014, announced his support for the New Hampshire senator's call to extend open enrollment in the exchanges and asked the administration to clarify how it would enforce the individual mandate.

"I read Senator Shaheen's letter today and support the common sense idea to extend the date for open enrollment. I believe, given the technical issues, it makes sense to extend the time for people to sign up," Pryor said in a statement Wednesday. "In addition, the Administration should state clearly how the enforcement mechanism will work if people can't sign up in time. We all want to see the law work, and I hope the Administration will take a hard look at this reasonable suggestion."

Sen. Joe Manchin, D-W.V., is working on a bill that would delay the $95 individual mandate penalty, a spokesman for Manchin said Wednesday.

Still, House Minority Leader Nancy Pelosi, who staked her speakership on the controversial vote, said the website's glitches are "disappointing," but she rejected calls from fellow Democrats to delay the law's implementation.

"Of course the situation right now is unacceptable, it's unfortunate, but we did not work very hard and many of us dedicate our public service to a website. It was to an initiative for affordable, quality health care," Pelosi, D-Calif., said. "What we want to do is fix it and go forward with it, not make policies that are predicated on its not working."

Members of the House Democratic Caucus were briefed Wednesday on the implementation of the Affordable Care Act by two officials from Centers for Medicare & Medicaid Services (CMS) - Gary Cohen, deputy administrator of CMS and director of Center for Consumer Information and Insurance Oversight, and Julie Bataille, director of the Office of Communications at CMS.

"They told us of all the work that's being done as a result of the president's urging to try to deal with some of the errors that were occurring with the website, how they've improved that, how they're moving forward with more access to phone coverage to give people access to that information," House Democratic Caucus Chairman Xavier Becerra, D-Calif., told reporters after the briefing. "At the end of the day, no process should bog down people getting a good product, to make sure that they have good-quality coverage on health insurance for their families."