WASHINGTON—Sen. Ron Johnson (R., Wis.) said he opposes the Senate Republican tax package, becoming the first GOP voice of dissent that, if it gains momentum, could force significant changes or jeopardize the party’s goal to pass the bill before the end of the year.

“If they can pass it without me, let them,” Mr. Johnson said in an interview Wednesday, adding that the plan unfairly benefits corporations more than other types of businesses. “I’m not going to vote for this tax package.”

Any Republican opposition is significant because GOP leaders 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.

Until now, no Senate Republican has come out definitively against the GOP tax plan. The risk for GOP leaders is that other Republicans get behind Mr. Johnson’s opposition, and either stop the bill or slow its passage, depriving Republicans of the chance to boost after-tax income household income next year, during the elections.