Senate Republicans are using the same procedures to move the tax overhaul through the chamber as they used this summer to try to repeal and replace the Affordable Care Act. In that effort, Republicans succeeded in voting to start debate, just as they did on Wednesday, but they could not ultimately muster the votes to approve a repeal bill.

To pass a tax bill in the Senate, Republicans will need the support of 50 of their 52 members, assuming no Democrats vote for the bill and Vice President Mike Pence breaks a 50-50 tie. The House already passed a tax package that differs substantially from the Senate’s version, so if the Senate can succeed in passing its bill, the two chambers would then need to reconcile the two plans.

But big changes could still be made to the Senate package in the next day or two. The Senate’s debate on the tax overhaul is limited to 20 hours, to be followed by a marathon series of amendment votes known as a vote-a-rama.

Two Republican senators, Ron Johnson of Wisconsin and Steve Daines of Montana, have been unhappy with how the Senate plan treats pass-through businesses, whose profits are distributed to their owners and taxed at individual income tax rates.

The current Senate plan allows pass-through owners to deduct 17.4 percent of business income as a way of lowering their tax rates. But Republicans now plan to lift the deduction to 20 percent, people familiar with the matter said.

Before Wednesday’s vote, Mr. Daines said that he had “seen enough progress to vote yes to move the debate forward,” alluding to the larger deduction.

“There has been some good progress for Main Street businesses in the tax cut bill,” he said. “I was able to secure more than $60 billion in tax cuts for Main Street businesses.”