Some top Senate Republicans are backing a change to the House ObamaCare replacement bill to increase financial assistance for low-income people to purchase health insurance.

Sen. John Thune John Randolph ThunePowell warns failure to reach COVID-19 deal could 'scar and damage' economy Senate Republicans signal openness to working with Biden Democrats scramble on COVID-19 relief amid division, Trump surprise MORE (R-S.D.), a member of Senate GOP leadership, said Tuesday he is working on an amendment to increase the tax credits under the bill for low-income people. Sen. Lamar Alexander Andrew (Lamar) Lamar AlexanderTrump health officials grilled over reports of politics in COVID-19 response Now is the time to renew our focus on students and their futures CDC says asymptomatic people don't need testing, draws criticism from experts MORE (R-Tenn.), chairman of the Senate Health Committee, and Sen. Roy Blunt Roy Dean BluntOn The Money: Trump undercuts GOP, calls for bigger COVID-19 relief package | Communities of color hit hardest financially by COVID-19 | Businesses, states pass on Trump payroll tax deferral Trump undercuts GOP, calls for bigger COVID-19 relief package Businesses, states pass on Trump payroll tax deferral MORE (R-Mo.), another Senate leader, said they support the idea as well.

The change would be significant — the House legislation, known as the American Health Care Act, currently bases its tax credits on age, meaning lower-income people do not get extra help, unlike under ObamaCare.

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“I do think there are things we can do to tailor the tax credit in a way that it makes more attractive to people and more helpful to people on the lower end and with a phaseout that is a little less steep than what the House has,” Thune told reporters Tuesday.

He added that he is working on an amendment to that end.

“It would be nice to add it to the House bill but if necessary, it could be in the Senate,” he said.

It is unclear how much the tax credits would be increased by.

While Thune has supported more help for low-income people in the past, the Congressional Budget Office (CBO) report on the GOP plan released Monday may be upping the pressure to provide more assistance: The report found that older people with low incomes would be particularly hard-hit by the bill.

In an extreme example, the premium for a 64-year-old making $26,500, after factoring in financial assistance, would rise from $1,700 to $14,600 under the GOP plan.

Alexander praised Thune’s proposed amendment and also called for increasing funding for the 10-year, $100 billion “stabilization fund” in the House bill that can help people afford premiums.

“I think there's some things we can do to improve it, including enlarging the stabilization fund for people with complex problems,” Alexander said. “Sen. Thune's working on amendment that would make the tax credit richer for lower-income people. I think both those things would be helpful.”

Blunt pointed to help for “older, lower-income people” in particular.

“We need to look at some things like people who are going to be least well-served in a new marketplace, is there a way to shift some of the opportunity of assistance toward them," he said.

The talk comes as a range of senators are calling for slowing down and making changes to the House bill, which is increasingly coming under fire.

But it is unclear how conservatives would feel about increasing the tax credits, which have already been a source of deep concern for them.