Republicans say they absolutely will not stand for any revenue increases in a sequester-replacement deal. But just a few weeks ago, the House GOP passed a bill that included one—a revenue hike that would prohibit illegal immigrants from receiving the refundable Child Tax Credit. The House's bill would have raised $7.2 billion, according to the Joint Committee on Taxation, and a stand-alone bill pushing the same reform was just introduced in the Senate last week by Sens. David Vitter (R-La.), John Boozman (R-Ark.), and Deb Fischer (R-Neb.).

Here's the issue at stake: The Child Tax Credit benefits many low-income families and was expanded in 2009 to raise the tax credit per eligible child to $1,000; beneficiaries also would qualify for a 15 percent tax refund on income earned above $3,000. (The recent fiscal cliff deal continues that expansion for another five years.) However, under current law, neither taxpayers nor their children have to provide a Social Security number to receive benefits; they can alternatively provide Individual Taxpayer Identification Numbers, which are issued by the Internal Revenue Service.

Republicans say that illegal immigrants have abused the system to receive the refundable tax credit from the government. They point to a 2011 report from the Treasury Department's Inspector General for tax administration, which said that unauthorized workers received $4.2 billion in refundable Child Tax Credits in 2010, recommending that the provision be changed. Republicans want to change the law to require a Social Security number to receive the refundable credit, casting the provision as a government handout given to tax cheats.

The change appears to be the only new tax-revenue increase in the House's 2012 sequester-replacement bill. But it's one that some of Congress' most conservative members are willing to support. "Call it a loophole, tax fraud, or government at its most outrageous, but it’s got to stop," Vitter wrote in an op-ed last year. "It’s not a tax deduction or credit that requires the recipient to actually pay any taxes. It’s a taxpayer-funded check from the federal government via the refundable Child Tax Credit program."

Elaine Maag, a senior research associate at the Urban Institute, points out that any beneficiary of the refundable Child Tax Credit would have to pay taxes on at least $3,000 in income in order to qualify for a refund. The IRS, moreover, has denied that the provision is a "loophole," saying the law was always meant to benefit those without Social Security numbers. But it also recently tightened the requirements for receiving an ITIN, making it harder for illegal immigrants to receive them.

So it's worth keeping in mind that the House GOP's own sequester-replacement proposal from 2012 does contain a tax revenue raiser—albeit one that targets low-income illegal immigrants. While it's uncertain whether the entire bill could even pass the House again, Senate conservatives like Vitter are keeping the issue alive in their independent efforts to target illegal immigration.