The House is expected to consider next week a bipartisan ObamaCare modification that failed to pass before the April recess.

The bill, sponsored by Rep. John CarneyJohn Charles CarneyDelaware becomes first state to ban child marriage Delaware lawmakers unanimously pass new gun control bill named for Beau Biden Overnight Energy: Coal miner deaths double in 2017 | EPA takes 7 Superfund sites off list | Delaware threatens to sue feds over air pollution MORE (D-Del.), would exempt Americans who work abroad and receive coverage through expatriate insurance plans from ObamaCare regulations.

While a majority, 257-159, voted for the bill on April 9, it did not meet the two-thirds majority requirement for it to pass under suspension of the rules. Since 52 Democrats supported the legislation, it stands a better chance of passing under a rule requiring only a simple majority.

The House has voted more than 50 times since 2011 to repeal or modify the healthcare law. Only a few dozen Democrats, at most, typically joined Republicans in those votes. But the larger-than-usual Democratic support, and the fact that a Democrat is sponsoring the bill, makes it more likely that the proposal could actually stand a chance of becoming law.

Carney said during floor debate earlier this month that requiring expatriate insurance plans to adhere to the healthcare law would give an advantage to foreign insurance companies that do not have to comply.

"It makes plans written in the U.S. more expensive, which gives companies an incentive to purchase foreign-based plans instead," Carney said.

But other Democrats objected to exempting certain insurance plans from the healthcare law.

"We should not advance a deeply flawed bill because an insurance company is making threats," said Rep. Henry Waxman (D-Calif.).