Nine Democratic senators and Independent Sen. Bernie Sanders introduced legislation Thursday to repeal an Obamacare tax on high-cost health insurance plans, adding their weight behind a rare bipartisan effort to change part of the healthcare law.

The bill would do away with the law's so-called "Cadillac tax," a steep new tax scheduled to kick in about two years from now. It would apply to health insurance plans where total spending exceeds $10,022 for an individual or $27,500 for a family. Surveys have estimated that it could affect as many as one-quarter of all employers who offer health benefits.

Republicans have long wanted to ditch the Cadillac tax, but now more Democrats are worried about how it could affect the ability of employers to offer cushier plans to those who want them. Hillary Clinton has called for repealing the tax as part of her presidential campaign. Sanders, who is also seeking the White House, signed onto the bill rolled out Thursday.

"Some have said that this tax only falls on 'Cadillac' health care plans, but the reality is that the plans this bill will tax are more like Chevrolets," Sanders said in a statement. "Workers have fought hard to negotiate decent healthcare benefits, often in exchange for lower pay. This excise tax unfairly punishes them. It has got to be replaced."

Sanders was joined by Democratic Sens. Sherrod Brown of Ohio, Chuck Schumer of New York, Patrick Leahy of Vermont, Mazie Hirono of Hawaii, Jeanne Shaheen of New Hampshire, Chris Murphy and Richard Blumenthal of Connecticut, Michael Bennet of Colorado and Bob Casey of Pennsylvania.

"We can control health costs while standing up for working Americans," Brown said. "By repealing the Cadillac tax, we can prevent certain employer-provided health plans from being taxed. But we shouldn't end one tax on middle class taxpayers while leaving them to foot the bill for an increase in the federal deficit."

But a big sticking point is how to make up the lost revenue from repealing the tax, which is expected to raise about $87 billion to help pay for the healthcare law. Democrats are likely to insist on paying for it, and they included a non-binding clause saying the bill should have an offset if it becomes law.