WASHINGTON — The Senate Republicans’ tax bill would leave millions of poor families with only partial access to a tax credit that conservatives have touted as a critical policy tool for alleviating poverty.

The measure Senate Republicans hope to pass this week expands a tax credit for parents, boosting it from the current maximum of $1,000 annually per child to $2,000 annually per child.

But despite urging from some conservative Republican senators, the bill would largely limit the benefits of its more robust “Child Tax Credit” to families who pay income taxes. That means the new increase would be almost entirely unavailable to working parents who only pay payroll taxes, which fund Medicare and Social Security, but do not make enough over the year to pay income taxes. The average annual salary of the family who would fail to qualify for the full increase in the benefit is $25,000, according to the Center on Budget and Policy Priorities, a left-of-center think tank.

While the plan would leave these poor families out of the full CTC, it would also extend it to some middle-class and upper-middle class families. Under current tax law, CTC’s benefits start declining once families make more than $110,000 annually. The latest Senate bill would expand eligibility to families earning up to $580,000 annually for married families with two children.

The upshot is that families in the middle and toward the top of the income distribution stand to gain significantly more from the CTC expansion in the Republican bill than the working poor. For example, a single mother with two children working a minimum-wage job would see her CTC benefit go up by $75 under the GOP bill. By contrast, a family with two children earning $500,000 annually would see its benefit expand by $4,000, CBPP said.

Two Republican senators, Marco Rubio of Florida and Mike Lee of Utah, have pushed for extending the credit in a way that would include low-income parents who don’t owe any income tax and still have a payroll tax burden, which is equal to 7.65 percent of income (the employer chips in an additional 7.65 percent). But it appears unlikely the final bill will include that expansion.

Under the Senate procedure Republicans plan to use to pass their bill, the bill can only add $1.5 trillion to the national deficit over a decade. And that cap, coupled with a plan to cut the corporate tax rate from 35 percent to 20 percent and scale back the estate tax paid exclusively by the very wealthy, has left the party with little wiggle room to expand other benefits.

“The payroll tax is completely left out of this discussion, and as a result about one-third of working families are left out of tax reform entirely,” said Samuel Hammond, a welfare policy analyst at the Niskanen Center, a libertarian-leaning think tank, who has helped spearhead a conservative effort for a more generous CTC. “It’s really disappointing,” Hammond said

For years, some conservative writers and activists have argued that CTC expansion could form a key piece of a conservative policy solution for alleviating poverty. The plan has support from many Democrats, too. While liberals tend to argue 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 Republican 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 both publicly and privately lobbying Senate Majority Leader Mitch McConnell, R-Ky., to make the tax credit fully refundable. On Monday, a few weeks after holding a news conference over the issue , he again tweeted out his support:

“To deliver a real tax cut for all Americans #TaxReformBill must make #ChildTaxCredit refundable for working families.”

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. (CBPP’s Chye-Ching Huang estimates it would cost about $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-Wyoming, chair of the Republican Policy Committee, which helps craft the party’s policy priorities, when asked if Republican leadership was considering the Rubio-Lee proposal. “We’ll have to see what the final package looks like.”

Senate Democrats charge that Republican leadership has 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.

But, Brown said of Republican leadership: “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.”

Lee and Rubio’s efforts have been met with backlash by the Wall Street Journal op-ed page, which recently excoriated Republicans trying to expand the Child Tax Credit. “Congress is preparing to maybe even double the Child Tax Credit. But what about couples who opted for dogs instead of children?” wrote one columnist.

Meanwhile, Rubio and Lee have also faced criticism on the left for not making their CTC expansion more generous. In particular, critics have noted that the Republican Senators would keep the CTC’s current phase-in structure, which means people who make more money in income get more from the tax credit.