WASHINGTON — A key part of House Republicans’ plan to overhaul the way corporations pay taxes is on life support, leaving lawmakers scrambling to save one of President Trump’s biggest priorities and increasing the chances the Republicans will simply pass a tax cut instead of overhauling the tax code.

A proposed tax on imports is central to the Republicans’ plan to lower the overall corporate tax rate. It would generate about $1 trillion over the next decade to finance the lower rates without adding to the deficit. It would also provide strong incentives for U.S.-based companies to keep their operations in the United States and perhaps persuade companies to move overseas operations to the U.S.

But the tax faces strong opposition from retailers, automakers and the oil industry, and a growing number of congressional Republicans have come out against it. They worry that it will increase the cost of imports, raising consumer prices.

Majority Leader Mitch McConnell, R-Ky., says there probably aren’t enough votes to pass the import tax in the Senate – not a single Republican senator has publicly endorsed it. And a powerful group of House conservatives says it’s time to dump the idea.

“The sooner we acknowledge that and get on with a plan that actually works and actually can build consensus, the better off we will be,” said Rep. Mark Meadows, R-N.C., chair of the conservative Freedom Caucus.

Even one of the biggest backers of the new tax says he is open to other ideas.

Rep. Kevin Brady, R-Texas, has pushed the tax as chairman of the House Ways and Means Committee. He still says it’s the best way to promote economic growth and domestic jobs, but he has softened his stance on alternatives.

“I’m still confident that we’re going to stay at the table until we solve that problem, which is how do we stop U.S. jobs from continuing to leave the United States,” Brady said. “We’re going to remain open to the best ideas on how we do that.”

On Tuesday, Brady proposed gradually phasing in the tax over five years.

It wasn’t received well by opponents.

“Forcing consumers to pay more so that some profitable companies can operate tax-free is no better of an idea in five years than it is today,” said Brian Dodge of the Retail Industry Leaders Association.

But if the import tax is dead, then what?

“I would never declare anything dead until there was a fully formed alternative,” said Rohit Kumar, a former tax counsel to McConnell who now heads PwC’s Washington tax office. “I think that’s one of the big challenges that Republicans are struggling with right now.”