WASHINGTON—Sen. Ron Johnson (R., Wis.) said he opposes the Senate Republican tax package, saying it unfairly benefits corporations more than other types of businesses.

“If they can pass it without me, let them,” Mr. Johnson said in an interview Wednesday. “I’m not going to vote for this tax package.”

Mr. Johnson’s position could undermine the Senate’s efforts to pass a tax plan by early December or get the bill to President Donald Trump’s desk by Christmas. Republicans are counting on near universal support from within the party to pass a bill on party line votes. With 52 seats in the Senate, Republicans can lose no more than two votes unless they can somehow find a way to win votes from Democrats.

Other Senate Republicans have expressed concerns. Jeff Flake of Arizona, for example, has worried about deficits and Susan Collins of Maine has worried about Republican plans to repeal the insurance coverage mandate in the Affordable Care Act as part of a tax overhaul.