The tax-reform bill that Senate Republicans are releasing Thursday does not repeal ObamaCare's individual insurance mandate, though the provision could be added down the line, GOP senators said.

Senators leaving a briefing about the legislation said repealing the mandate is not in the initial text of the legislation, but cautioned that the issue is still under discussion.

"There's been a lot of discussion on that and we're looking at it very seriously," Sen. John Hoeven John Henry HoevenDavis: The Hall of Shame for GOP senators who remain silent on Donald Trump Bottom line Bipartisan senators seek funding for pork producers forced to euthanize livestock MORE (R-N.D.) said, adding that the issue was discussed at Thursday's meeting.

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Hoeven said he personally supports repeal of the mandate.

An updated House tax-reform bill unveiled Thursday by House Ways and Means Committee Chairman Kevin Brady Kevin Patrick BradyBusinesses, states pass on Trump payroll tax deferral Trump order on drug prices faces long road to finish line On The Money: US deficit hits trillion amid pandemic | McConnell: Chance for relief deal 'doesn't look that good' | House employees won't have payroll taxes deferred MORE (R-Texas) also does not repeal the mandate.

Senate Republican leaders have been doing a whip count on repealing the ObamaCare penalty to see where support stands. Sen. John Cornyn John CornynCalls grow for Biden to expand election map in final sprint Bipartisan praise pours in after Ginsburg's death Chamber of Commerce endorses McSally for reelection MORE (R-Texas), the No. 2 Senate Republican, said lawmakers are taking a "hard look" at the issue.

Proponents of nixing the mandate say it is a way to save money that could help pay for tax cuts. The Congressional Budget Office (CBO) says mandate repeal would save $338 billion over 10 years.

But moderates like Sens. Susan Collins Susan Margaret CollinsJeff Flake: Republicans 'should hold the same position' on SCOTUS vacancy as 2016 Trump supporters chant 'Fill that seat' at North Carolina rally Momentum growing among Republicans for Supreme Court vote before Election Day MORE (R-Maine) and Lisa Murkowski Lisa Ann MurkowskiMomentum growing among Republicans for Supreme Court vote before Election Day Collins: President elected Nov. 3 should fill Supreme Court vacancy Barrett seen as a front-runner for Trump Supreme Court pick MORE (R-Alaska) have expressed reluctance to repeal the mandate. Introducing the volatile issue of health care into the tax debate could made it harder to pass the bill.

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Still, many Republican senators say they want the change.

Sen. Ted Cruz Rafael (Ted) Edward CruzVideo of Lindsey Graham arguing against nominating a Supreme Court justice in an election year goes viral Sunday shows preview: Justice Ginsburg dies, sparking partisan battle over vacancy before election Democrat on Graham video urging people to 'use my words against me': 'Done' MORE (R-Texas) pushed for the idea when leaving the meeting on Thursday.

Cruz did not say how he would vote on the current bill, saying discussions are "ongoing."

Repealing the mandate would result in 13 million more uninsured people over 10 years, according to the CBO, and could destabilize health insurance markets.