A growing chorus of Senate Republicans wants the bigger tax cuts for individuals and families in their tax overhaul, but the problem remains how to pay for it. And their leader says the biggest pot of money is in repealing the individual mandate to purchase health insurance. 

“We’re optimistic that inserting the individual mandate repeal would be helpful and that’s obviously the view of the Senate Finance Committee Republicans as well,” Senate Majority Leader Mitch McConnell of Kentucky said Tuesday. 

One of his deputies, Senate Republican Conference Chairman John Thune of South Dakota, said the repeal of the mandate would be part of a modified version of the tax overhaul the Senate Finance Committee would consider. 

“Yeah, it’ll be distributed in the form of middle-income tax relief, it will give us even more of an opportunity to really distribute the relief to those middle-income cohorts who could really benefit from it,” Thune said. 

Watch: Who Gets to Write the Tax Bill?

Some Republicans, like Sen. Susan Collins of Maine, have expressed concerns that including health care provisions in the tax bill could complicate its passage.

“That’s under very active consideration. My concern is that if we combine the health care issues with the tax reform we make it far more controversial,” Collins said.

The Congressional Budget Office recently estimated that repealing the mandate would lower the federal deficit by $338 billion over the next 10 years, but also result in 13 million fewer people with health insurance and premium hikes of 10 percent per year. 

Meanwhile, as the Finance Committee awaits full details of the GOP proposals, there are several other ways Republicans could free up additional revenue, but none appear to have the full backing of the conference. 

Soliciting broad support for any major revisions could be difficult, as several GOP members are already content with the changes the bill would already make to the individual tax code.

“I’m pretty happy with where we are,” said Sen. Shelley Moore Capito of West Virginia.

But some Republican lawmakers want to go further.

“My most significant concern with current drafts is they don’t do enough to reduce taxes on the individual side. I believe we should be cutting taxes for every taxpayer. And an outcome where we are raising taxes on a significant number of Americans is unacceptable,” Sen. Ted Cruz, R-Texas, said.

The Joint Committee on Taxation found that the Republican framework released last week by Senate Finance Chairman Orrin G. Hatch of Utah would produce tax cuts for each income bracket in every year over the next 10 years.

But some could also see their taxes remain the same, or even experience a tax increase under the GOP plan.

“In 2019, based on JCT’s distribution tables as many as 14 million Americans with incomes under $200,000 can expect to see a tax increase and another 36 million can expect to see almost no tax change,” Tom Barthold, chief of staff at the office of the congressional scorekeeper, said on Tuesday.

Members have floated raising the corporate tax rate above the proposed 20 percent or repealing the mandate in the 2010 health law that requires individuals to purchase insurance.

While some lawmakers have expressed support for providing less tax relief to corporations to provide greater tax cuts to individuals and families, others — including most members of the Finance panel — say the lower business tax rate is the bigger priority.

“I think that would be a big mistake,” Sen. Patrick J. Toomey, R-Pa., said of hiking the corporate rate. “A very, very important part of what makes this work is a 20 percent tax rate that is permanent.”

Meanwhile, repealing the individual mandate comes with its own problems. The GOP can only afford to lose the support of three of its members — assuming no Democrats support the tax measure. Some members may raise concerns that removing the mandate could undermine the current law and lead to higher health care costs.

Other tax relief proposals have been kicked around as well. 

Sens. Marco Rubio, R-Fla., and Mike Lee, R-Utah, have pushed for a greater child tax credit. The proposal released last week by the Finance Committee hikes the $1,000 per child credit to $1,650; Rubio and Lee want it increased to $2,000.

“It is simply not enough for working families,” the senators said in a joint statement last week. “The Senate is not going to pass a bill that isn’t clearly pro-family, so we look forward to working with our colleagues to get there.”

Senate Republicans could also roll back their full repeal of the state and local tax deduction, a move that may be necessary anyway to appease House Republicans. The House measure included a $10,000 limit on property tax deductions to try to get support members from high-tax states like New York and California who oppose removing the SALT deduction.

That approach could appease some skeptics in the Senate.

“If we did the House approach … I think that would be a good way to improve the distribution of the benefits of the tax bill,” Collins said.

In order to meet the requirements for the budget reconciliation process Republicans are using to advance a bill with only GOP support, no provision can add to the federal deficit outside of the 10-year budget window.

The Senate Finance Committee is expected to release an updated chairman’s mark on Tuesday to address the so-called Byrd Rule.

Andrew Siddons and Jennifer Shutt contributed to this story.