By voting to open debate on a temporary extension of long-term jobless benefits, Republicans gave themselves leverage to force Democrats to consider cuts from elsewhere to pay for it.

But so far, the GOP has failed to come forward with a plan Democrats could support.

Senate Majority Leader Harry Reid told CQ Roll Call he has yet to see an offer from the GOP he could take seriously. Reid has said he would prefer not to offset the emergency extension, but would consider proposals that he viewed as genuinely bipartisan efforts.

“Not yet. They’ve offered to go after Obamacare and go after little kids, so you know, those two aren’t too good,” the Nevada Democrat said.

The most recent GOP offer to pay for the extension came Wednesday from Sen. Kelly Ayotte, R-N.H., who suggested Congress pay for unemployment benefits — plus a rollback of approved cost of living adjustment cuts for veterans’ pensions — by eliminating child tax credits filed by undocumented workers. Seven Republican senators stood by her side, touting its ingenuity. Republican Saxby Chambliss, R-Ga., even dubbed the plan “all-American,” evoking laughs from the other senators on stage.

The idea of eliminating that credit isn’t new, and Democrats have panned it before. Sen. David Vitter, R-La., introduced the Child Tax Credit Integrity Preservation Act of 2011 in March of that year and the Child Tax Credit Integrity Preservation Act of 2013 last January.

He and Senate Budget Committee ranking member Jeff Sessions, R-Ala., have been championing the idea for years. Sessions — who discussed the measure on the floor Wednesday — offered it as an amendment to the immigration bill in a Judiciary Committee markup, where it failed on a party-line vote. The Vitter bill never had more than three listed co-sponsors in either session of Congress.

But the Democrats’ bigger issue with the proposal is just who would be affected by eliminating the “loophole” created by not requiring Social Security numbers to qualify for the Additional Child Tax Credit. Any person born in the United States is by Constitutional definition a United States citizen, even if their parents are not. According to a Pew Hispanic analysis in 2010 (the most recent of its kind), more than 4 million American-born children of undocumented parents lived in the U.S. — nearly 80 percent of all children of undocumented immigrant parents under the age of 18. Therefore, the elimination of this tax credit would affect 4 million American citizens, who are minors.

Democrats never would support such a trade, and instead they have floated the notion of paying for an extension of jobless benefits with savings from a potential farm bill compromise.

Republicans indicated Wednesday that such a proposal was not currently under discussion among farm bill conferees.

Earlier this week, Senate Minority Leader Mitch McConnell, R-Ky., said Republicans would vote in high numbers to extend the jobless benefits if Democrats paid for it by delaying the individual mandate — the heart of their health care law — by one year.

Of the six Republicans who voted to advance the three-month bill Tuesday, three have declared publicly they may vote to block the bill if it doesn’t have offsets. As Roll Call reported earlier, Sen. Susan Collins, R-Maine, was the only Republican at the Ayotte news conference Wednesday who discussed the issue of how to approach a more permanent reform of the long-term, federal unemployment insurance program.