Sen. Susan Collins, R-Maine, has not yet said she will back the legislation, either.
The stances of both Rubio and Lee could change if Republican leaders make tweaks to the bill. They aim to boost the refundability level of the credit and effectively make more families eligible for it.
The bill that passed the Senate would increase the child tax credit to $2,000 per child, refundable up to $1,100. The credit is currently $1,000.
Rubio and Lee pushed Senate negotiators to increase the child tax credit to that level from an initially proposed $1,650. They still want to expand the measure to allow more working families to qualify for it.
"As it's currently structured, it's only $1,100, which means a lot of people making 35, 40, 25 thousand dollars working are not going to be able to utilize as much of the credit as they need. And so what I've asked is that $1,100 be raised," Rubio told reporters Thursday.
"Unless they can figure out a way to add to the $1,100 figure I won't support the bill," he added.
Senate Finance Committee Chairman Orrin Hatch, R-Utah, told Bloomberg later Thursday that he did not know what Senate leadership would do to appease Rubio. He told the news outlet that Republicans "probably" can approve the legislation even if Rubio votes against it.
House and Senate negotiators are hammering out a deal on a final tax bill that both chambers hope to pass next week and send to President Donald Trump for his signature. Passing a tax bill by the end of the year is a key goal for Republicans, who want a legislative achievement to promote ahead of next year's midterm elections.
Complicating matters is the health of GOP Sens. John McCain, R-Ariz., and Thad Cochran, R-Miss., who have missed votes this week. McCain is undergoing treatments related to brain cancer. Cochran reportedly had a nonmelanoma lesion removed from his nose but is available for votes next week.
Vice President Mike Pence has delayed a planned Middle East trip amid the Senate's push to pass the tax legislation. He could have to vote to break a tie in the Senate if two Republicans vote against the plan.