Sen. Dianne Feinstein announced Tuesday evening she is co-sponsoring an Obamacare bill by fellow Democratic Sen. Mary L. Landrieu that would allow individuals to keep their original health insurance coverage.

“I have decided to cosponsor Senator Mary Landrieu’s legislation: Keeping the Affordable Care Act Promise Act. This bill provides a simple fix to a complex problem. This bill will extend the grandfather date for individual insurance plans so that individuals who have insurance policies they like can keep them indefinitely, unless the individual chooses another plan or the insurer stops providing health insurance in the individual market,” Feinstein said in a statement.

“Since the beginning of September, I have received 30,842 calls, emails and letters from Californians, many of whom are very distressed by cancellations of their insurance policies and who are facing increased out-of-pocket costs,” Feinstein continued. “I believe consumers should be allowed to choose their plans, and they should be adequately informed about those choices. Consumers must be told what their coverage does and does not include so families don’t find themselves paying for an insurance policy they believe is comprehensive when in fact it is not.”

Landrieu is up for re-election in Louisiana in 2014, as are two of her bill’s five co-sponsors — Democrats Kay Hagan of North Carolina and Mark Pryor of Arkansas. She urged House Democrats to vote against a similar bill from Rep. Fred Upton, R-Mich., saying that his bill would not indefinitely keep the president’s promise that Americans who liked their health insurance plan could keep it. House Democrats expect some defections on the Upton bill later this week, but on Tuesday all House Democratic leaders announced their opposition to the House measure.

Last week, in-cycle Senate Democrats had a serious venting session at the White House with President Barack Obama — airing their concerns regarding the troubled health care law rollout and the potential ramifications for their re-election chances.

Landrieu told a small group of reporters Tuesday night that the White House has not said “no” but it also has not said “yes” to her suggested changes. She emphasized that she still is supportive of the law and that any change she suggests is borne out of a desire to make the law work.

“There is great promise for the Affordable Care Act, despite the setbacks, despite the trouble with the rollout, with the website. The promise for Americans — wealthy, middle class and poor — to have insurance they can never lose, that they can count on every day of their life, that will be there for them and their families and their children, a bill that will virtually eliminate medical bankruptcies in this country, is worth fighting for,” Landrieu said.