WASHINGTON — As D.C. enters week two of the government shutdown, House Democrats find themselves in a very strange position: Most of them have now voted against funding nutritional assistance for women, national parks, the District of Columbia, pay for the National Guard, FEMA, veterans benefits, and cancer research at the National Institute of Health.

And they'll tell you they are just fine with that.

Congressional Democrats have said from the beginning of the shutdown that they would not settle for anything short of a clean funding bill that reopens the entire government without any strings attached. Republicans have responded by introducing a series of narrow bills that would fund specific, highly visible parts of the government and nothing else. The GOP's strategy is to force Democrats to vote against funding popular programs — thus convincing the public that the party of President Obama is being unreasonable.

"Hard to believe, but 164 Democrats voted against WIC yesterday. They would rather keep gov. shutdown than support WIC," tweeted Republican Rep. Renee Ellmers after a House vote on funding nutritional assistance program during the shutdown.

Comments like that have left Democrats — who have long championed programs like WIC (Women, Infants, and Children) — infuriated and baffled to say the least. But they are also confident that no amount of Republican messaging can shift public opinion against them as the shutdown drags on.

"Everything that was up is now down, everything that was left is now right. It seems like it's a bizarre divide and conquer strategy," said Democratic Rep. Eric Swalwell. "The tea party is maybe repenting for years of neglecting poor hungry children or veterans. It does feel like we're in a strange land right now."

Rep. Keith Ellison, one of the most outspoken progressives in the House, said even the vote to fund WIC was an easy one for him to oppose.

"No, it's not hard because I know it's not going anywhere," he said. "People in my district and districts all over this country know who is for food stamps, they know who is for WIC, they know who is for education. [Republicans] cannot switch their identity that miraculously. They wanted to cut $40 billion out of food stamps two weeks ago. They are trying to get Democrats on bad votes. The American public isn't stupid."

"I don't think anyone buys that Democrats are the heartless ones in Washington," said Rep. Joe Crowley, a member of the Democratic leadership in the House.

It's an uphill strategy for the GOP, considering it was Republicans who set the government on the path to a shutdown when they first insisted that any bill to fund the government would have to also defund or delay Obamacare. There's now no clear plan for an end game. As one Republican lawmaker told The Washington Examiner last week, "We're not in a situation that has been planned out and war-gamed and plotted."

But in the short term, the latest strategy has caused a few dozen Democrats to buck party leadership on the piecemeal bills, giving Republicans some bipartisan cover. It also prompted an unforced error by Senate Majority Leader Harry Reid when he was asked about funding for cancer patients at a press conference. So far, the House has passed seven mini-funding bills, all of which Reid has said he won't take up and the president has threatened to veto.

And talk to any Republican and you'll get virtually the same message : We've done something to end the shutdown. They haven't.

The exception to that pattern is a bill that guarantees furloughed workers will receive back-pay once the shutdown ends, which the president has signaled he will sign. A bill that guarantees pay for the troops was passed and signed into law before the government shutdown.

Democrats said Republicans' strategy resemble the successful one the GOP employed during the sequester battle, during which progressives effectively caved. This time, they say, they won't make the same mistake.

"Their strategy for sequester was to try and piecemeal it. They thought they could have their cake and eat it too. They are trying to have that same cake now with the shutdown," said Democratic Rep. Steve Israel. "The sequester was damaging enough, but a shutdown of the entire government of the United States of America is a completely different matter. We're not interested in continuing a game."

The face-off will continue this week with the added pressure of a deadline for hitting the debt ceiling on Oct. 17. House Speaker John Boehner said on ABC this Sunday that the House doesn't have enough votes to pass clean continuing resolution despite the fact that more than 20 Republican members have signaled they'd vote for one with House Democrats should the bill ever come to the floor.

"Let me issue him a friendly challenge. Put it on the floor Monday or Tuesday. I would bet there are the votes to pass it. We have just about every Democrat, 21 Republicans have publicly said they would. There are many more Republicans who have said that they privately would," said Sen. Chuck Schumer, who followed Boehner appearance on ABC. "So, Speaker Boehner, just vote. Put it on the floor and let's see if you're right."

But if the last week was any indication, that's not going to happen. Instead, the House will continue to take up the piecemeal bills: On Monday they'll vote on one to keep the FDA running during the shutdown, and later in the week one that funds Head Start educational programs. Boehner has continued to insist that it is the president and Senate Democrats who are responsible for keeping the government closed because they refuse to negotiate.

"[I]t's my way or the highway. That's what he's saying. Complete surrender and then we'll talk to you," Boehner said of Obama. "It's about having a conversation. I gave the Senate majority leader some advice at the White House about how to proceed. I gave him some advice over a week ago about how to avert this. And yet they refuse to do it."