Sen. Mary Landrieu said Wednesday she would propose legislation to ensure all Americans could keep their existing insurance coverage under Obamacare, a fresh sign of the political problems the law’s rollout has created for congressional Democrats.

Landrieu, a Democrat who faces a tough reelection in Louisiana in 2014, said she would either offer her own bill or formally sign onto another measure that would ensure that the law would not force anyone off of their existing health policies.

“The promise was made, and it should be kept,” Landrieu said in the Capitol Wednesday. “And it was our understanding when we voted for that bill that people when they have insurance could keep with what they had. So I’m going to be working on that fix.”

Landrieu’s comments come as the White House faces a barrage of criticism over President Barack Obama’s repeated promises in 2009 that the law would not force anyone off of their plans.

But since the online marketplaces were rolled out this month, insurance companies have sent hundreds of thousands of letters warning policy holders in the individual marketplace that they would be kicked off their plans. The White House has argued that this cancellation only affects 5 percent of consumers in the individual marketplace, and that they would in turn be able to select better coverage plans than their current policies.

Nevertheless, the unequivocal promises Democrats made in 2009 have emerged as a political liability for the White House and Democrats in Congress. And some like Sens. Joe Manchin, a Democrat from the red state of West Virginia, and Sen. Jeanne Shaheen (D-N.H.), who faces reelection next year, have either called for an extension of the enrollment period or a delay of major elements of the law.

In September 2010, all Senate Democrats, including Landrieu, voted to reject a plan Republicans said would have killed Obama administration regulations that now have resulted in the cancellation of insurance policies.

Landrieu said that her bill would “grandfather” in soon-to-be-cancelled plans, even if insurance holders could find better policies through the exchanges.

Asked if she believed Obama wasn’t forthright with the public about the law, Landrieu said: “I didn’t think it was intentional” and said that the country would be “better off” if Republicans had tried to improve the law rather than repeal it repeatedly.

Responding to criticisms that she was taking the action to protect herself politically, Landrieu said of Republicans: “These guys will make up anything — always have. And I’ve beat them every time, and I intend to do it again.”