Rep. Patrick MurphyPatrick Erin MurphyEx-Dem lawmaker: My vote in Florida wasn’t counted due to signature issues Voters are not thinking about consumer confidence at the polls, says pollster Republicans saying they should run on economy aren't talking to real voters, says pollster MORE (D-Fla.), a top Republican target for 2014, has signed on as a sponsor of legislation that would allow people to keep their health insurance plans under ObamaCare.

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Murphy is only the third Democrat to back the bill, following Reps. John BarrowJohn Jenkins BarrowThe most important runoff election is one you probably never heard of Our democracy can’t afford to cut legal aid services from the budget Dem files Ethics complaint on Benghazi panel MORE (D-Ga.) and Mike McIntyreDouglas (Mike) Carmichael McIntyreGOP picks up retiring McIntyre's seat in NC Seven Dems vote to create Benghazi panel Lawmakers prep for big race on Sunday MORE (D-N.C.), who are also vulnerable in the midterm elections.

Both Barrow and McIntyre voted against the healthcare law in 2010.

Murphy's office could not be reached for comment.

The "keep your plan" bill has picked up increasing support since introduced and now has 161 co-sponsors. A vote on the bill is set for Friday.

Rep. Paul RyanPaul Davis RyanJordan on leadership loss: 'We knew it was an uphill fight' McCarthy defeats Jordan for minority leader in 159-to-43 vote The Hill's 12:30 Report — Sponsored by Delta Air Lines — Leadership elections in Congress | Freshman lawmakers arrive | Trump argues he can restrict reporter access MORE (R-Wis.) has also signed on as a co-sponsor, potentially giving cover to some conservative Republicans wary of backing a bill that fixes ObamaCare, rather than dismantling it fully.

House Democrats are largely opposed to the measure, however. House Minority Whip Steny Hoyer (D-Md.) said Tuesday he’s leaning toward opposing the bill but emphasized that he hasn’t seen the final version yet.

And the White House has come out against the bill, with spokesman Jay Carney on Tuesday arguing that allowing Americans to keep their current plans would sabotage the minimum coverage requirement in the new healthcare law.

Still, the thousands of Americans facing dropped coverage due to ObamaCare have prompted bad press and national backlash against the president and Democrats, who have seen the political advantage they saw post-shutdown erased in the wake of the rocky ObamaCare rollout.