President Donald Trump and top congressional tax writers say they want to prevent undocumented workers from claiming tax breaks they aren’t entitled to by tightening up the standards, but a proposal to expand the use of Social Security numbers is finding resistance among lawmakers, including Republicans who are worried about identify theft.

Trump’s fiscal 2018 budget request would expand on language in the 1996 tax overhaul that required tax filers claiming the earned income tax credit to include a qualifying child’s name and Social Security number on the return. The administration said it would tighten the mandate to require such filers to also show they have the right to work.

The budget proposal would also add a requirement that filers claiming the child tax credit have a Social Security number and demonstrate a right to work in the U.S.

The administration says that a number of taxpayers with Social Security numbers who are claiming the EITC do not have approval to work in the country.

House Ways and Means Chairman Kevin Brady of Texas and Senate Finance Chairman Orrin G. Hatch of Utah both said an emerging tax overhaul could be a vehicle for measures similar to the administration’s proposals. The administration says it would save $40 billion over 10 years.

“That will be dealt with in tax reform,” Brady said last week.

Administration officials such as Attorney General Jeff Sessions have linked efforts to prevent bogus claims for tax breaks to other enforcement measures aimed at addressing illegal immigration.

But the revenue-raising proposal in the administration’s budget request faces strong Democratic opposition and parts of it drew a skeptical response from senior GOP senators such as Roy Blunt of Missouri and Michael B. Enzi of Wyoming, who point to bipartisan support for efforts to delete — rather than mandate — Social Security numbers in documents and electronic files in order to prevent identity theft.

The worry about data theft is much greater than it was in 1996, when the Social Security number was required to claim the earned income tax credit.

“We’ve clearly got to look at all of the pay-fors in the president’s budget. Many of them will be unacceptable. And some of them, like this one, are debatable,” Blunt said.

“I think there’s some problems with using Social Security numbers,” Enzi said.

The Internal Revenue Service estimates that 27 million families received $67 billion through the earned income tax credit in tax year 2015, while the child tax credit provided about $60 billion in benefits to about 35 million families.

According to a 2011 study by the Treasury inspector general, people not authorized to work in the U.S. received $4.2 billion in refundable child tax credit payments in 2010. There is no data available on fraudulent use of the earned income tax credit.

Massachusetts Rep. Richard E. Neal, ranking member of the House Ways and Means Committee, said many Democrats would oppose Social Security number mandates because of concerns they would deter eligible taxpayers from claiming tax breaks and invite theft by hackers. “I don’t think it’s necessary,” Neal said.

Critics of the president’s proposal are also worried about the effect it would have on claimants.

“It would take benefits away from children,” said Rep. Luis V. Gutierrez, D-Ill. The Center on Budget and Policy Priorities, a liberal think tank, has called for other measures to address fraud and overpayments, such as a testing mandate for tax preparers, and tougher penalties for fraud.

While the administration and senior Republicans consider Social Security number mandates, a number of Republicans say they are undecided.

Colorado Sen. Cory Gardner, chairman of the National Republican Senatorial Committee, predicted many Republicans would be open to measures to fight tax cheats, but would also want safeguards against identity theft. For example, he said he would push for action on his own proposal that would require agencies to specifically decide whether Social Security numbers are necessary in mailed federal documents and require regulations that allow redactions of personal data.

“I think there is a way to crack down on fraud within the EITC, and use that to expand additional EITC opportunities,” Gardner said. He referred to bipartisan proposals to provide the credit to workers without children.

In the House, Rep. Sam Johnson, R-Texas, has sponsored a bill that would require the Social Security number of a single taxpayer — or one of two spouses on a joint return — in order to claim the refundable version of the child tax credit.

It would raise an estimated $20 billion over 10 years, according to a Joint Committee on Taxation score of a similar bill in the last Congress.

Last week, Brady’s panel approved a similar proposal by Pennsylvania GOP Rep. Lou Barletta to require Social Security numbers to qualify for subsidies and tax credits under the House-passed proposal to repeal and replace parts of the health care overhaul. It is expected to move as a stand-alone bill in the House, and represents a potential add-on to the broader health care legislation now pending in the Senate.