Sen. Mary Landrieu (D-La.) says she's pushing forward with her bill, despite President Obama's announcement.

In a statement after Obama's remarks, Landrieu said that she will continue to work on legislation to allow people to keep their insurance plans, even after Obama said he will look to fix the problem administratively.

"I’m encouraged that the President took action to stop the cancellation of insurance policies that people were promised they could retain," Landrieu said in a statement. "I was particularly happy to see the notification provision included, which is an important part of my bill. I will be working today and throughout the weeks ahead to support legislation to keep the promise."

Landrieu's bill has so far attracted the support of five other Senate Democrats: Joe Manchin (W.Va.), Dianne Feinstein (Calif.), Jeff Merkley (Ore.), Mark Pryor (Ark.) and Kay Hagan (N.C.).

Hagan reportedly said she will continue to support Landrieu's legislation as well.

There is a similar measure in the House led by Rep. Fred Upton (R-Mich.) and a competing measure in the Senate led by Sen. Mark Udall (D-Colo.).

While the administration's plan would allow insurance companies to re-instate canceled plans for one addition year (subject to approval by the states), Landrieu's would require insurers to maintain any plan that exists as of Dec. 31,2013, as long as the consumer meets the requirements and pays his or her premiums. Under Landrieu's bill, these plans could conceivably remain in effect indefinitely, rather than just one year.