WASHINGTON–Mitt Romney‘s opposition to a $5.2 billion wind tax credit is roiling Capitol Hill, where wind-state Republicans are scrambling to figure out how to save the credit without exposing sharp differences with their party’s presidential candidate.

Republicans and Democrats had agreed to include the tax break, known as a production tax credit, in a package designed to extend expiring business tax breaks. But after Mr. Romney came out against the tax credit, Republicans were put in a tough spot. The result: The tax credit was omitted from a tax-extenders plan announced shortly after midnight that is to be voted on Thursday in the Senate Finance Committee.

By Wednesday, the fate of the wind tax credit was in flux. One possible scenario is that Senate Finance Committee Chairman Max Baucus (D., Mont.) could restore the tax credit on Thursday, when he unveils a modified version of the tax extenders package. “There might be a few modifications that I might offer at the markup as I’ll present a chairman’s modification,” Mr. Baucus told reporters. Asked whether that could include the wind tax credit, he said “it could include anything.”