Republican Sens. Marco Rubio of Florida and Mike Lee of Utah plan to offer an amendment to the Senate version of the GOP tax bill to ensure that low-income families can still benefit from the child tax credit even if they don't make enough money to pay income taxes.

“We have a chance to do better by working families in this tax bill," Rubio and Lee said in a joint statement announcing their intention to offer the amendment Wednesday.

The current Senate bill would increase the child tax credit from $1,000 today to $2,000, and make it available at higher levels of income. But families with no taxable income would get limited benefits from the change because the bill would only slightly increase the refundable portion of the credit — that is, the part that the government will effectively send as a check to these families.

Ten million children in families with low earnings would only get a token benefit of $75 or less from the increase in the credit in the current Senate bill, according to the Center on Budget and Policy Priorities.

The senators said their amendment will make the credit refundable against payroll tax liability, which low-income families do pay. It would also index the credit to inflation, and eliminate the marriage penalty.

The benefit would be paid for by raising the corporate rate from 20 percent to 22 percent in the bill.

Although Democrats are currently united against the bill, some may be tempted to vote for an amendment that traded a higher corporate rate for bigger tax credits for lower-income families. On the other hand, Democrats might stand united against such an amendment if passing it meant that Rubio and Lee would vote "aye" and provide a majority for the underlying bill. Those dynamic could complicate vote-counting on the Senate floor.

Republican leaders are likely to change the bill before it is introduced on the Senate floor through a manager's amendment, before voting on amendments begins. Republicans aim to begin voting on the bill later Wednesday, and hope to pass it by Friday.