The disastrous rollout of President Obama's health care law rollout has damaged the 2014 re-election prospects of Democratic lawmakers, a series of polls shows.

A survey released Tuesday by CNN/Opinion Research is the seventh poll in just over two weeks to show Democrats having lost the edge they gained with voters during a government shutdown blamed on Republicans.

The latest poll shows Republicans leading Democrats on the generic ballot, 49 percent to 47 percent. It follows two polls by Rasmussen, one by Fox News and another by Quinnipiac University that document a major shift away from Democrats since the glitch-plagued rollout of Obamacare began on Oct. 1.

Democrats just a month ago enjoyed as much as a 9 percentage point lead among voters, thanks in part to Republican efforts to defund the health care law, which resulted in a 16-day government shutdown.

At the time, Democrats were exuberant about the resulting backlash against the GOP over the shutdown. But the party's advantage is gone now, polls show.

"The Democratic lead," CNN reported, "has disappeared."

Can Democrats get it back, or has the unpopular law paved a path to victory for the GOP in 2014?

Democrats could regain favor with voters, say political analysts, under a number of scenarios, including another government shutdown battle in December and January, when lawmakers face critical spending deadlines.

Though leaders on both sides insist there will not be another shutdown, another closing is possible because the temporary funding measure keeping the government open expires on Jan. 15 and must be replaced. Voters tend to blame congressional Republicans for that kind of gridlock on Capitol Hill.

"Do Republicans shoot themselves in the foot, or do they handle it better this time," said Jennifer Duffy, senior editor at the Cook Political Report, which analyzes political races.

The political fate of the Democrats, meanwhile, remains tied to the success of Obamacare. Cancelled insurance policies, higher premiums and deductibles and major problems shopping for plans on the health care exchanges have made the law unpopular and is causing problems for Democrats who voted for it.

The most vulnerable red-state Democrats seeking re-election have suffered the most at the polls.

Sen. Mary Landrieu, D-La., was already facing a competitive race for a fourth term next year. The problems with the health care law, including nearly 100,000 policy cancellations in her state, contributed to a 10 percentage point drop in her approval ratings, a Southern Media and Opinion Research poll shows.

Re-election bids by Sens. Kay Hagan, D-N.C., and Mark Pryor, D-Ark., have also been hurt by the health care law. Hagan lost a nearly 17-point lead over her GOP opponents since the Obamacare rollout began.

Republican campaign operatives are fueling criticism of Democrats and Obamacare with advertising targeting vulnerable Democrats in more than a dozen House districts.

One GOP campaign brochure mockingly quotes Democratic National Committee Chairman Debbie Wasserman Schultz, who pledged that the party would campaign on the success of the new health care law and win seats in 2014. The brochure includes fake talking points for Democrats, including this advice, "The best thing to do is step in front of the camera and explain to Americans why the government should run their health care."

Americans United for Change, a group, is defending the new law, sending an email Tuesday that claimed problems with the rollout are decreasing. The email included links to news stories highlighting Obamacare success stories.

"The system is improving, enrollment is increasing, more consumers are smiling, horror stories are failing, and health costs are shrinking," Americans United for Change spokesman Jeremy Funk said.

But more bad news may be lurking for the website, including the prospect of employers next year dropping employee health plans and pushing millions of additional people into the new health care exchanges.

"These poll numbers may stick," Duffy said. "It's a real problem for Democrats. Because I don't think the rollout is the problem with the health care law, I think the problems are much bigger."