It was a victory for the White House and the bipartisan group of senators who had spent months negotiating it.
Voting continued in the 100-seat chamber, where the timing of a final vote on passage remained unclear.
The chamber’s top Republican, Mitch McConnell, had previously signalled his support for the bill.
“Republicans and Democrats have radically different visions these days, but both those visions include physical infrastructure that works for all of our citizens,” Mr McConnell said.
“The investments this bill will make are not just necessary, in many cases, they are overdue. Our country has real needs in this area.”
Progress has been held up by a flurry of disagreements over demands for new Defence Department improvements and a bill provision on cryptocurrency.
Senator Bill Hagerty also baulked after the nonpartisan Congressional Budget Office said on Thursday that the legislation would increase federal budget deficits by $256 billion over 10 years.
Mr Hagerty was former president Donald Trump’s ambassador to Japan before replacing former senator Lamar Alexander.