Sen. Dianne FeinsteinDianne Emiel FeinsteinLawmakers feel pressure on guns Feinstein: Trump must urge GOP to pass bump stock ban Florida lawmakers reject motion to consider bill that would ban assault rifles MORE (D-Calif.) on Tuesday became the fifth Senate Democrat to formally call for a rewrite of ObamaCare so people who like their health insurance can keep it.

Feinstein announced that she would join Sen. Mary LandrieuMary Loretta LandrieuProject Veritas at risk of losing fundraising license in New York, AG warns You want to recall John McCain? Good luck, it will be impossible CNN producer on new O'Keefe video: Voters are 'stupid,' Trump is 'crazy' MORE's bill, the Keeping the Affordable Care Act Promise Act.

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"The Affordable Care Act is a good law, but it is not perfect," she said. "I believe the Landrieu bill is a commonsense fix that will protect individuals in the private insurance market from being forced to change their insurance plan. I hope Congress moves quickly to enact it."

Late last week, Sens. Kay HaganKay Ruthven HaganPolitics is purple in North Carolina Democrats can win North Carolina just like Jimmy Carter did in 1976 North Carolina will be a big battleground state in 2020 MORE (D-N.C.) and Mark PryorMark Lunsford PryorMedicaid rollback looms for GOP senators in 2020 Cotton pitches anti-Democrat message to SC delegation Ex-Sen. Kay Hagan joins lobby firm MORE (D-Ark.) joined the bill. Those two and Landrieu are in tight re-election races next year, but Feinstein and the fifth cosponsor, Sen. Joe ManchinJoseph (Joe) ManchinPavlich: The claim Trump let the mentally ill get guns is a lie Toomey to introduce bill broadening background checks for firearms Scott Walker backs West Virginia attorney general in GOP Senate primary MORE (D-W.Va.), are not up for re-election until 2018.

Feinstein said she is joining the bill after receiving thousands of calls and letters from angry constituents who may lose their health coverage.

"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," she said.

Feinstein's support is just the latest blow to President Obama, who last week was forced to acknowledge that millions of people are being told their insurance plans would be canceled because they don't meet ObamaCare's new standards.

Those cancelation notices go against Obama's explicit and repeated promise that if people like their insurance plan, they can keep it under the law. Feinstein said Congress must ensure that this promise is kept.

"Too many Americans are struggling to make ends meet," she said. "We must ensure that in our effort to reform the health care system, we do not allow unintended consequences to go unaddressed."

Her support is a sign that support for a legislative fix is growing even among Democrats. That factor could end up forcing Obama to accept some changes to the law, although White House Spokesman Jay Carney indicated today that Obama is leaning more toward finding ways to make it more affordable for people to use new plans that meet ObamaCare's standards.

At the same time, however, the House is expected to vote Friday on GOP legislation that is similar to Landrieu's, and some Democrats are likely to support that bill.