Republican Sens. Marco Rubio Marco Antonio RubioMurky TikTok deal raises questions about China's role Sunday shows preview: Justice Ginsburg dies, sparking partisan battle over vacancy before election Florida senators pushing to keep Daylight Savings Time during pandemic MORE (Fla.) and Mike Lee Michael (Mike) Shumway LeeMcConnell shores up GOP support for coronavirus package McConnell tries to unify GOP Davis: The Hall of Shame for GOP senators who remain silent on Donald Trump MORE (Utah) said Wednesday that they plan to offer an amendment to the Senate tax bill to further expand the child tax credit and pay for doing so by slightly raising the bill's corporate tax rate.

Under the amendment, the child tax credit would become refundable up to the payroll tax liability of 15.3 percent of earnings, allowing more low-income families to be able to take advantage of it.

The amendment would also fix a marriage penalty associated with the credit and index the credit to the same inflation index that other individual tax changes are tied to under the bill.

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These changes would offset by raising the corporate tax rate in the bill from 20 percent to 22 percent. The corporate tax rate is currently 35 percent.

The current version of the Senate bill increases the child tax credit from $1,000 to $2,000, but Rubio and Lee have been pushing to expand it even more. The senators have been advocating an expansion of the child tax credit for years, and have gotten Ivanka Trump, the president's daughter and adviser, behind their efforts.

Rubio and Lee said they are offering their amendment to give families a bigger percentage of the bill's tax relief.

"Right now, 70 percent of the tax cuts we’re considering would go to businesses, and only 30 percent to individuals. This amendment would level the playing field for families, while still kick-starting national investment and growth," they said in a statement. "By increasing access to the Child Tax Credit, we can increase working family fairness and deliver overdue relief to America’s greatest investor class: our moms and dads.”

The White House said Wednesday it opposes the proposal.

“[We support] the child tax credit. We also think that it’s important to make businesses more competitive. We would not support raising the corporate rate as outlined in that amendment," spokesman Raj Shah told reporters aboard Air Force One.

The Senate is expected to vote later on Wednesday to begin debate on the tax bill. Lawmakers will be able to offer amendments when the bill is being debated.

- This story was updated at 2:10 P.M. EST.