Rep. Paul Ryan (R-Wis.), chairman of the House Budget Committee (Win McNamee/GETTY IMAGES)

In fact, Ryan was moving ahead with a GOP bill that would actually slash programs that aid the poor — proposing a $33 billion cut to food stamps, for instance — to replace automatic reductions of defense spending that were part of August’s debt-ceiling deal. But House Republicans insist that such cuts actually show a cool-headed, warm-hearted approach to poverty. By battling waste, fraud and abuse in social programs, they explain, Republicans can make the government more effective at helping Americans who are actually in need.

It’s logic that seems hard to argue with: Who, after all, thinks that a lottery winner should be on food stamps for two years after she netted $1 million? The reality is that the new Republican bill does take steps to close loopholes and eliminate redundant programs. But the Republicans’ sequester replacement does much more than target waste and fraud in social programs. It cuts aid to those who are legitimately receiving benefits.

At Monday’s budget markup, Republicans firmly rejected the notion that the cuts will actually hurt the poor. “Taking food from children? Not true,” declared Rep. Marlin Stutzman, a freshman Republican from Indiana, sitting at the paper-clogged table where the House committee was finalizing its version of the sequester replacement. His words echoed Ryan’s response to earlier attacks from Catholic bishops and activists who accused his budget of “crucifying” the poor.

As the deliberations dragged into the night, the GOP lawmakers doubled down on their line that they want to give aid to those who qualify, and that their bill simply aims to target scammers gaming the system and bureaucrats oblivious to government waste.

The House GOP proposal “does not change the eligibility criteria for SNAP one bit,” declared Ryan, who shed his jacket as the meeting wore on. “Where in the government do we have waste? Should prisoners be getting SNAP benefits? Should lottery winners getting SNAP benefits?...People eligible for the benefits should get them. It shouldn’t go beyond that.”

Back at home, the public “hears about lottery winners receiving food stamps, and we sit here hearing about taking food out of the mouths of babes,” added Rep. Tim Huelskamp (R-Kansas).

Ryan is correct that the House Republicans’ newest budget doesn’t radically reform eligibility standards for programs like food stamps. Rather, the bill accelerates the phase-out of a stimulus program that raised benefits for all food stamp beneficiaries. It was originally scheduled to expire at the end of 2013, but the GOP bill would halt the program immediately, cutting benefits by $57 per month. It would also eliminate a provision that allows states to offer food stamps to Americans whose incomes are just slightly above the limit for assets.

The bill, however, would reduce benefits for nearly all households that receive food stamps — about 44 million in total — and would cut them off entirely for 2 million who are currently qualified for food assistance, according to the left-leaning Center on Budget and Policy Priorities, at a time when unemployment remains above eight percent.

There’s a legitimate argument about which Americans should receive food stamps and how much they should receive. But the GOP legislation doesn’t eliminate fraud or abuse. It eliminates or reduces benefits to Americans who legitimately received them.

The Republicans are also proposing cuts aimed at closing loopholes that both parties agree should be closed. At the hearing, Rep. Tim Huelskamp (R-Kan.) brought a giant check to illustrate a loophole that allows states to spend just $1 on home-energy assistance to get beneficiaries up to $1,560 in food aid from the federal government, as the District of Columbia has recently done.

“They make people eligible when they aren’t qualified....and we can’t find 4 percent to cut?” Huelskamp said, waving the check in the air.

The provision was, in fact, originally intended to make needy citizens eligible for more food assistance. It lets poor Americans who already receive aid to heat their homes — through the Low Income Home Energy Assistance Program — get a deduction that helps them qualify for more food aid.

Senate Democrats on the Agriculture Committee have proposed raising the states’ contribution to $10 a year. But House Republicans want to eliminate the provision entirely, which would reduce food stamp benefits for about 1.3 million households by $90 month, according to the Congressional Budget Office.

Republicans do follow through on their promise to reduce what they believe are “duplicative programs.” The bill would cut a job-training program administered by SNAP to food-stamp beneficiaries by 72 percent. The logic is that the government funds many other job-training programs, so this particular one is redundant. But critics point out that it’s unclear whether people who had to leave one program after it closed would necessarily find assistance in another program.

House Democrats raised harsh objections during Monday’s markup of the budget bill. “Why are we picking on food stamps?” Rep. Earl Blumenauer (D-Ore.) asked the room. “We should not be cutting benefits for 46 million people in order to deal with occasional lottery winner. What are the odds there?”

Blumenauer and his colleagues were pushing for an amendment that would restore the cuts to food aid in the budget bill. And for a split second, he even seemed to win over Ryan. When the clerk asked the budget chairman whether he’d vote for his fellow lawmaker’s amendment—reversing his position on food stamps— Ryan was absorbed in a side conversation and caught unprepared.

“Ay —” Ryan suddenly stopped himself. “No!” He chuckled, smiling at his Democratic colleagues. “Almost got me, almost got me.”

House Republicans defeated Blumenauer’s amendment, 13-19, and passed the rest of the sequester replacement a few hours later.