Sen. Dianne Feinstein, a Democrat who usually backs the Obama administration but displays an independent streak from time to time, is joining forces with Sen. Mary Landrieu, D-La., on a bill that allows people in jeopardy of losing their individual health plans to keep them.

"This bill provides a simple fix to a complex problem," Feinstein said in a Tuesday statement announcing she would co-sponsor Landrieu's bill. "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."

Hundreds of thousands of people with insurance plans in the individual market have received cancellations notices because their plans no longer comply with Obamacare's minimum benefit requirements. Millions more are set to lose their plans if the government doesn't alter or delay the health care law, undermining President Obama's oft-repeated promise to the American people that they could keep their plans if they liked them.

The Senate's red-state Democrats who are up for re-election next year are pressuring the White House and Democratic leaders to take up similar legislation addressing the so-called grandfathered plans.

Feinstein’s addition to the bill gives it more political weight, if not political traction. So far, the Senate Democratic majority has refused to take up legislation altering the health care law in the wake of the botched roll-out.

Sen. Tom Harkin, D-Iowa, who chairs the Senate health panel, continues to resist any changes to the health care law. He told reporters Tuesday there's no need for a delay because Americans are just procrastinating and will eventually sign up.

In the first month Massachusetts offered a government-brokered health care option, 123 people signed up, he said.

"People are going to wait — they're going to wait to see what's happening out there. There's a lot of confusion going on and they have until March 31 to sign up," he said.

Republicans who run the House will pass their own bill to tweak the law this week, which will likely attract at least some Democratic support.

But Landrieu Tuesday said the measure, sponsored by Rep. Fred Upton, R-Mich., who chairs the Energy and Commerce panel, is aimed at unraveling Obamacare while her version is trying to find a real solution to those shocked to be losing their coverage.

Landrieu told reporters that Upton’s bill creates a "loophole so big you could drive a Mack truck through it.” She said it offers a chance for more people to have access to individual health care plans that insurance companies offered before the health care law was enacted and only allows people to keep their current plans for one year.

"It has a one-year cut-off so it's not really keeping the promises," which she said is "an important promise that we should find a way to keep."

"So I am hoping that the Democrats in the house will vote no because the Upton bill is not a fix that will keep the promise," she said. "It's disguised as a fix, but it really undercuts the Affordable Care Act. My bill will not."