WASHINGTON -- Throughout the budget showdown, the mantra of tea party Republicans, led by Sen. Ted Cruz (R-Texas), has been "make DC listen."

On Twitter, the Senate floor and in repeated interviews on Capitol Hill and on Fox News, Republicans have stressed their connection to the people and small-d democracy.

"I just think you saw members who said, 'Look, let’s just do what we all know needs to be done and frankly what the American people want to see done,'" said Rep. Jim Jordan (R-Ohio), a conservative wing leader, after this weekend's critical House GOP meeting.

"Sometimes I go back to basic civics: We're the House of Representatives. We're the body that's supposed to be closer to the people," Jordan said. "That's why the Founders gave a chance for the people to throw us out every two years."

But there is a critical flaw in Republicans' argument that they are just carrying out the will of the people: If the House of Representatives -- the "People's House" -- was allowed by GOP leaders to work its will by casting a straight up-or-down vote on the bill passed by the Senate to avert a government shutdown, that bill would become law.

And that, more likely than not, is how this will end. The only question is when.

Shortly after House Republicans unveiled their latest gambit targeting Obamacare in exchange for funding the government, Rep. Charlie Dent (R-Pa.) went off-script by throwing his support behind the Senate bill, which is known as a clean continuing resolution, because it continues government funding without major amendments to other legislation.

"Let's see what the Senate sends back," Dent told reporters Saturday. "If they send back another clean CR, I suspect -- again, I'm not making a decision on what's going to be on the floor -- a clean CR would likely to be on the floor at some point."

"I’m prepared to vote for a clean resolution tomorrow," he added Sunday, according to The New York Times' Jonathan Weisman. "It’s time to govern. I don’t intend to support a fool’s errand."

Rep. Tom Cole (R-Okla.), deputy majority whip of the House, told reporters that the decision to pass a clean government funding bill belonged entirely to House Speaker John Boehner (R-Ohio).

"He didn't mention it, but I'm sure he could if he wanted to," Cole said as he emerged from Saturday's meeting.

"We're pretty much out of options at this point,'' said Rep. Devin Nunes (R-Calif.). "They're all giddy about it. You know who benefits the most here from a shutdown? The Democrats benefit and they know that."

Rep. Peter King (R-N.Y.), a vocal critic of Cruz's do-or-die approach, pinned his hopes on 'normal people' finding a way to avert a shutdown.

"I don't want to be undercutting anything that's going on. I'm hopeful normal people are going to prevail," he said. "There's still time for the Senate to act."

Even those insisting they would support nothing less than a one-year delay of Obamacare conceded there were enough votes to pass a clean continuing resolution in the final hours.

"I think there's enough people in the Republican Party who are willing to do that. And I think that's what you're going to see," Rep. Raul Labrador (R-Idaho) said on NBC's "Meet the Press," while maintaining that he himself would oppose such a measure.

There are currently 200 Democrats in the House, meaning that only 17 Republicans would be needed to win a majority and pass a clean bill. And while Republicans control the chamber, it is not quite as close to the people as Jordan says. In the 2012 election, Democratic candidates for the House received more votes than Republicans.

Senate Majority Leader Harry Reid (D-Nev.) has repeatedly insisted -- and demonstrated through bipartisan votes -- that no bill that makes changes to Obamacare will get through the upper chamber as part of the shutdown fight.

Republicans have not yet uniformly absorbed that lesson, but many observers believe the government actually shutting down will be an opportunity for a teachable moment.

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  • The Numbers

    The House has 233 Republicans and 200 Democrats. Each party should pick up one more seat when two vacancies are filled. Going into the election, the GOP edge was 242-193. Senate Democrats will have a caucus of 55, including two independents, Angus King of Maine and Bernie Sanders of Vermont. Republicans have 45. That's a pickup of two seats for Democrats. <em>(Text <a href="http://www.huffingtonpost.com/huff-wires/20130103/us-new-congress-glance/">via the Associated Press</a>)</em>

  • Women

    The House will have 79 women, including 60 Democrats. At the end of the last session, there were 50 Democratic women and 24 Republican women. The new Senate will have 20 women members, an increase of three. That consists of 16 Democrats and four Republicans. The last Senate had 12 Democratic women and five Republicans. (Text <a href="http://www.huffingtonpost.com/huff-wires/20130103/us-new-congress-glance/">via the Associated Press</a>)

  • Freshmen

    With two vacancies to be filled, the House has 82 freshmen; 47 Democrats and 35 Republicans. As of the end of the last session, 87 of 103 freshmen were Republicans. The Senate will include 14 new faces, with nine Democrats and the independent King. Five are women. New senators include Brian Schatz, who was sworn in on Dec. 27 to fill the seat of the late Hawaii Democrat Daniel Inouye. (Text <a href="http://www.huffingtonpost.com/huff-wires/20130103/us-new-congress-glance/">via the Associated Press</a>) <em>(Pictured at left: Incoming House freshmen of the 113th Congress pose for a group photo on the East steps of the Capitol in Washington, Thursday, Nov. 15, 2012. AP Photo/Susan Walsh)</em>

  • African Americans

    The House will have 40 African-Americans, all Democrats. The number of Democrats is unchanged, although two Republicans will be gone: Allen West, R-Fla., lost his re-election bid, and Tim Scott, R-S.C., was appointed to fill the Senate seat of Jim DeMint, R-S.C., who is retiring. Scott will be the first black lawmaker in the Senate since Roland Burris, who retired in 2010 after filling the Illinois Senate seat of Barack Obama for almost two years. (Text <a href="http://www.huffingtonpost.com/huff-wires/20130103/us-new-congress-glance/">via the Associated Press</a>) <em>(Pictured at left: Rep. Tim Scott, R-S.C., who was appointed by South Carolina Gov. Nikki Haley to replace outgoing Sen. Jim DeMint, R-S.C., walks out of the Republican policy luncheon on Capitol Hill in Washington, Tuesday, Dec. 18, 2012. AP Photo/Susan Walsh)</em>

  • Hispanics

    The new House will have 33 Hispanics, with 25 Democrats and eight Republicans. That's up slightly from last year. The Senate will have three Hispanics: Democrat Robert Menendez of New Jersey, Republican Marco Rubio of Florida and Republican freshman Ted Cruz of Texas. (Text <a href="http://www.huffingtonpost.com/huff-wires/20130103/us-new-congress-glance/">via the Associated Press</a>) <em>(Pictured at left: Rep.-elect Joaquin Castro, D-Texas, speaks with members of the media after a news conference with newly elected Democratic House members on Capitol Hill in Washington, Tuesday, Nov. 13, 2012. AP Photo/Pablo Martinez Monsivais)</em>

  • Other Minorities

    The new House will have nine Asian Americans, all Democrats. There are two American Indians: Tom Cole, R-Okla., and Ben Lujan, D-N.M. (Text <a href="http://www.huffingtonpost.com/huff-wires/20130103/us-new-congress-glance/">via the Associated Press</a>) <em>(Pictured at left: Sen.-elect, current Rep. Mazie Hirono, D-Hawaii, and her husband, Leighton Oshima ride the Senate Subway on Capitol Hill in Washington, Tuesday, Nov. 13, 2012. AP Photo/Harry Hamburg)</em>

  • Other Facts

    According to CQ Roll Call newspaper, the average age of House members in the 113th Congress is 57; the average age of senators is 62. It estimates that the House will include some 277 Protestants and Catholics, 22 Jews, two Muslims and two Buddhists. The Senate will have 80 Protestants and Catholics and 10 Jews. The House will have its first Hindu, Rep.Tulsi Gabbard, D-Hawaii. Senate freshman Mazie Hirono, also of Hawaii, will be the Senate's only Buddhist and its first Asian American woman. Also for the first time, white men will be a minority among House Democrats. (Text <a href="http://www.huffingtonpost.com/huff-wires/20130103/us-new-congress-glance/">via the Associated Press</a>) <em>Pictured at left: Rep.-elect Tulsi Gabbard, D-Hawaii is seen on stage during a news conference with newly elected Democratic House members, on Capitol Hill in Washington, Tuesday, Nov. 13, 2012. AP Photo/Pablo Martinez Monsivais)</em>