Analyses suggest many lower- and middle-class families could eventually see higher tax burdens, as benefits for families expire.
Republicans can afford to lose just two members of their party, and are scrambling to secure support for a final vote on the plan by the end of the week.
Mr McCain had appeared to be on the fence about the proposal, and worried about its effect on the deficit.
But in a statement on Thursday he said: “This is not a perfect bill, but it is one that would deliver much-needed reform to our tax code, grow the economy and help Americans keep more of their hard-earned money.”
If the bill passes the Senate, lawmakers will have to craft a compromise bill with the House in a process known as going to “conference committee”.
This is a normal process that occurs when the House and Senate approve similar but slightly different bills.
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