WASHINGTON—Sen. John McCain said he would support a $1.4 trillion tax cut that Republicans are advancing in the Senate, pushing the plan closer to passage though intense jockeying is still playing out among lawmakers as a critical vote on the Senate floor nears in the hours ahead.

The support of the Arizona Republican, who helped defeat GOP efforts to repeal major parts of the Affordable Care Act this year, gives Republicans momentum. Party leaders want to pass the bill this week. They still haven’t locked down all the needed...