So far, five Senate Democrats are on record in support of legislation by Sen. Mary Landrieu, D-La., to make sure everyone can keep their present coverage if they want to. The bill would require insurance companies to continue offering existing policies, even if they fall short of minimum coverage requirements in the law.
The measure has little apparent chance at passage, given that it imposes a new mandate on the insurance industry that Republicans will be reluctant to accept.
At the same time, a vote would at least permit Democrats to say they have voted to repair some of the problems associated with the Affordable Care Act, as many appear eager to do.
In a statement, Landrieu said Sens. Jeff Merkley of Oregon, Kay Hagan of North Carolina and Mark Pryor of Arkansas were now supporting the legislation, as is Sen. Dianne Feinstein of California. All but Feinstein are on the ballot next year.
Across the Capitol, majority Republicans in the House set a vote for Friday on legislation to permit insurance companies to continue selling existing policies that have been ordered scrapped because they fall short of coverage standards in the law.
While House passage of the measure is assured, each Democrat will be forced to cast a vote on the future of a program that Republicans have vowed to place at the center of next year's campaign.
Democratic Rep. Mike Doyle of Pennsylvania, who voted for the initial Obama health care bill, said Thursday that members of his caucus want an opportunity to go on the record in support of allowing people to keep the insurance they had.
Doyle told MSNBC in an interview that at a White House meeting Wednesday, House Democrats told Obama about "the frustration level that many of us have" with the health care roll-out.