As glitches with the Obamacare website continue, more Democrats are joining the chorus calling for changes to the law's implementation. (The Washington Post)

For weeks congressional Democrats maintained a united front during the battle over the budget and debt ceiling limit, but when it comes to the problems plaguing the new health care law, the fissures are far more visible. While the divisions are still relatively minor -- most of the lawmakers involved are calling for modest changes, and have emphasized their commitment to making the system work--they show that the administration has a limited amount of time to fix the enrollment process before many Democrats see it as a political liability in 2014.

On Friday 10 senators, lead by Sen. Jeanne Shaheen (D-N.H.), asked Health and Human Services Secretary Kathleen Sebelius to extend the program's enrollment period beyond March 31 to ensure Americans aren't penalizing for failing to sign up for insurance by then. Four of the signatories -- Sens. Mark Begich (D-Alaska), Mark Pryor (D-Ark.), Mary Landrieu (D-La.), Kay Hagan (D-N.C.) -- are top Republican targets next year in conservative states, while another, Michael Bennet (D-Colo.), is likely to face a significant challenge in 2016. Shaheen and Sen. Mark Udall (D-Colo.), another co-signer, are also on the ballot in 2014, but are less imperiled.

And separately, Sen. Joe Manchin (D-WVa.) is working with Sen. Johnny Isakson (R-Ga.) to press for a one-year delay in the individual mandate that Americans buy insurance, which is seen as a more direct challenge to the law because insurances have based their rate estimates on a certain number of Americans enrolling by the spring.

In an interview Thursday night, Manchin said he only wants to work with colleagues who are "sincere" about making the law work.

"I’m not giving up. You have to make it better," he said. "All we’re postponing is the crime and a fine" on taxpayers who don't register for insurance.

When looking at the politics around the Affordable Care Act, it's important to keep in mind that people's views vary dramatically, depending on the state in which they live. The Kaiser Family Foundation released a paper this spring based on tracking polls between April 2010 and March 2013 that found public attitudes toward the law were much more hostile in states such as West Virginia, Louisiana and Alaska, compared to those in New England and on the West Coast.

In West Virginia, the favorable-unfavorable ratio was 30 percent to 50 percent; in Alaska it was 33 percent to 46 percent; and in Louisiana, 33 percent to 52 percent. In other words, the law was a hard sell even before the enrollment glitches emerged this month.

Still, Democrats aren't in outright revolt. If the system can be fixed quickly, Democrats will feel much less nervous. But for now, Rep. Gerry Connolly (D-Va.) noted in an interview, "The stakes are high because of the politics of it."

And it's not going to get any easier as 2014 approaches.