Ivanka Trump walks with Sen. Marco Rubio (R-Fla.) after a meeting with other senators on Capitol Hill in June. (Melina Mara/The Washington Post)

The Senate Republican tax plan would leave out millions of the poorest families from expanded child tax credits, but Republican Sens. Marco Rubio (Fla.) and Mike Lee (Utah) are pushing a plan to include those families — and to pay for it by taking some proposed tax breaks away from corporations.

The Senate Republican bill would expand what's known as the “Child Tax Credit,” boosting it from the current maximum of $1,000 annually per child to $2,000 annually per child. But that increase is largely limited to families who make enough money to pay income taxes. Families who don't make enough for income taxes and instead pay only payroll taxes wouldn't qualify for the full increased credit and instead would get only an additional $75 annually per child.

Rubio and Lee on Wednesday proposed changing the Senate bill to extend more of the new benefit to such families, by lowering the level of income at which the benefit begins to kick in, extending more in new credits families who don't pay income taxes.

To offset the new tax benefits for the poor, Rubio and Lee's amendment would raise the bill's proposed corporate tax rate. The current corporate tax rate is 35 percent, but, as written, the Senate bill would drop that to 20 percent. Rubio and Lee proposed instead dropping it to 22 percent.

Rubio and Lee also want to raise revenue by phasing out the new benefit at a lower income level than the bill proposes. Under current tax law, CTC’s benefits start declining once families make more than $110,000 annually, but the bill would expand eligibility to some families earning up to $580,000 annually. The Rubio-Lee amendment would phase that out at $250,000, another change that would help offset expanding the tax credits for low-income families.

The pair's plan faces an uphill battle as the Senate prepares to vote on a final bill. Rubio and Lee join a list of senators asking for changes. President Trump has been adamant about a 20 percent corporate tax rate, and the pair would have to convince colleagues to take tax benefits from corporations and the upper middle class.

If they succeed, they'd accomplish a long-held goal among some conservatives who've argued that the child tax credit expansion could form a key piece of a policy solution for alleviating poverty. The plan has support from many Democrats, too. While liberals tend to argue that poverty should be addressed by greater spending on domestic social programs, 46 Senate Democrats have also endorsed a plan to expand the CTC.

Conservatives are not hiding their frustration with the current Senate bill.

“It needs to be equal opportunity tax relief,” said April Ponnuru, a senior adviser at the Conservative Reform Network. “There are lots of hard-working Americans out there who deserve a tax cut. If conservatives want to stand for tax relief, how can they ignore the main tax that most families pay?”

With the help of Ivanka Trump, Lee and Rubio have had some success in moving the GOP bill in their direction. Since it was introduced in the House, the CTC’s proposed maximum benefit has increased steadily to $2,000. The Senate bill also raises the age at which children are eligible for the credit to 17 from 16.

“At each stage of the process, the tax reform bill has gotten better at returning more money to hard-working families,” Lee said. “I will continue to push the bill in that direction with a particular focus on making the CTC refundable up to payroll tax liability.”

Like Lee, Rubio has been lobbying Senate Majority Leader Mitch McConnell (R-Ky.) to make the tax credit fully refundable. Given that several Republican senators are threatening to withhold their support from the tax bill on other issues, however, it’s not clear what would drive McConnell to agree to the Rubio-Lee plan. McConnell does not have much money to throw around; the CTC expansion would be expensive; and both Lee and Rubio are already expected to vote yes on the bill. (Chye-Ching Huang, deputy director of federal tax policy at the nonpartisan Center on Budget and Policy Priorities, estimates it would cost $70 billion to incorporate the Rubio-Lee plan’s proposed expansion of the CTC for low-income Americans.)

“There’s so many things that are still to be decided,” said Sen. John Barrasso (R-Wyo.) when asked if Republican leadership was considering the Rubio-Lee proposal. “We’ll have to see what the final package looks like.” Barrasso is chair of the Republican Policy Committee that helps craft the party’s policy priorities.

Senate Democrats charge that in the current bill Republican leaders have cut off a potential bipartisan deal on a crucial issue. “Lee and Rubio have been genuinely interested in this and done it in good faith,” Sen. Sherrod Brown (D-Ohio) said. “They’re not serious about the Child Tax Credit. The senator’s kid gets a full refund, but a family making $30,000 with two kids doesn’t.”