Murkowski, a key moderate swing vote, wrote in the Fairbanks Daily News-Miner that she supports giving people additional freedom by repealing the mandate, which requires people to have health insurance or pay a fine.

"Repealing the individual mandate simply restores to people the freedom to choose," Murkowski wrote. "Nothing else about the structure of the [Affordable Care Act] would be changed."

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She contrasted the provision with GOP ObamaCare repeal bills earlier this year, which she said went too far by restructuring Medicaid and making other changes.

Murkowski voted against those earlier bills. She was one of three GOP senators to help defeat a "skinny repeal" bill in July, which had the central component of repealing the mandate.

Murkowski did not mention the tax bill in her written piece on Tuesday , but her support for repealing the mandate indicates she would not object to including that provision in the tax bill.

She said she worried that insurance is not affordable for some people, who are then being fined for going without coverage by the mandate.

"People have been forced out of the market by the high cost of insurance, with some often forced to pay a tax because the price of insurance was too high for them to afford," she wrote.

"While I support repealing the individual mandate, I strongly support enacting the bipartisan compromise Alexander/Murray legislation into law as fast as possible to stabilize our markets, provide more control to states and more choices to individuals," she wrote.

Insurers and many health policy experts warn that the market would be destabilized and premiums would rise without a mandate because fewer healthy people would sign up, leaving just sicker and costlier people.

The Congressional Budget Office estimates premiums would rise 10 percent but markets would remain stable in almost all areas of the country without a mandate.