WASHINGTON ― Millions of parents would get bigger tax refunds in the coming months from a bill the House of Representatives could vote on this week.

The House Ways and Means Committee approved the legislation last week by a vote of 40 to 3, with all Republicans in support.

The bill would likely pass the House in a similarly overwhelming bipartisan fashion ― but only if House Speaker Mike Johnson (R-La.) allows the vote to happen in the face of a likely right-wing backlash.

It’s the same conundrum Johnson has faced with other legislation, such as bills to avoid government shutdowns. If Johnson allows the House to vote on something bipartisan, then far-right members of the House Freedom Caucus might retaliate against him for collaborating with Democrats.

Lawmakers were put on notice Monday by Republican leadership that the House could vote on the tax bill this week. If the bill passes the House, it’s unclear if it will sail through the Senate or meet more resistance from Republicans there.

The measure pairs a temporary $30 billion expansion of the child tax credit with about $30 billion of business tax cuts. Over the next two years, certain tax filers will receive larger refunds, especially low-income parents of multiple children. Some 16 million children would benefit, according to an analysis by the Center on Budget and Policy Priorities.

If Congress sends the bill to President Joe Biden’s desk in the coming weeks, then the IRS would likely be able to send out bigger refunds to low-income parents claiming the credit this tax season, said Alison Flores, manager of the Tax Institute at H&R Block.

“We don’t expect to see more people eligible, but those who are ― especially at the lower income ranges ― will get more benefit because of that expansion of the refundable portion,” Flores said.

The Joint Committee on Taxation, one of the lawmakers’ in-house legislative scorekeepers, estimated that a taxpayer with two qualifying children and an income of $9,000 for last year would get a child tax credit refund worth $975 under current law but $1,950 if Congress enacts the Tax Relief for American Families and Workers Act, as the bill is known.

Bigger refunds for a few million households are a far cry from Democrats’ vision for the child tax credit, which in 2021 they temporarily changed into a monthly allowance worth as much as $3,600 per child annually. The proposal under consideration doesn’t significantly boost the $2,000 value of the credit; instead, it gradually increases the amount that can be paid back as a refund. Last year, the refundable portion of the credit topped out at $1,600.

Some progressives have grumbled that the changes won’t do enough to reduce child poverty. “At a time when a majority of American voters believe a tax on big corporations should be increased, there is no reason we should be providing corporations a tax cut while only giving families pennies,” Rep. Rosa DeLauro (D-Conn.) said Monday.

The bill may face stronger criticism from the right. Freedom Caucus member Rep. Scott Perry (R-Pa.) complained on Friday, for instance, that the legislation will allow “illegal foreign nationals” to claim the credit, even though the bill does not change the requirement for children to have social security numbers to qualify.

“The Child Tax Credit reforms in this bill are pro-family policies that maintain the child tax credit structure of the Trump-era GOP tax reform,” Ways and Means chair Jason Smith (R-Mo.), who negotiated the bill with Senate Finance chair Ron Wyden (D-Ore.), said in a statement pushing back on the criticism. “It halts any push for monthly checks and provides no special loopholes for illegal immigrants.”