Whether the government shuts down likely depends on the outcome of a civil war in the Republican Party over health care, a tussle on full display Wednesday as House Republicans openly fought with their GOP counterparts in the Senate.

It's left President Obama and Democrats in Congress to watch from the sidelines as it all plays out.

The GOP internecine brawl spilled into the open after Sen. Ted Cruz, R-Texas, publicly admitted that the Senate can't pass the government funding resolution that the House plans to vote on Friday because it would strip funding for the president's health care law -- despite his public support for that approach.

"[Senate Democratic Majority Leader] Harry Reid will no doubt try to strip the defund language from the continuing resolution, and right now he likely has the votes to do so," Cruz said in a statement.

Cruz, who's been a leading voice pushing to "Defund ObamaCare," tried to kick responsibility back to the lower chamber, which will have to vote again on whatever the Senate does pass.

"At that point, House Republicans must stand firm, hold their ground, and continue to listen to the American people," Cruz said.

Reaction from House members was swift -- and nasty.

"House agrees to send #CR to Senate that defunds Obamacare. @SenTedCruz & @SenMikeLee refuse to fight. Wave white flag and surrender," Rep. Sean Duffy, a conservative sophomore Republican from Wisconsin, wrote on Twitter.

"So far Sen Rs are good at getting Facebook likes, and townhalls, not much else. Do something..." Rep Tim Griffin, R-Ark., tweeted.

It's frustration driven by the reality that the House GOP could take the brunt of the blame if the government does shut down -- even though it's Cruz and a handful of other Republican senators who are leading the charge to use the government funding bill to defund ObamaCare. Sens. Mike Lee and Marco Rubio also issued statements on Wednesday praising House Speaker John Boehner for scheduling a vote on a government funding bill that included the defund ObamaCare provisions.

Boehner's move was a cave to his party's right-wing -- House leaders had originally planned to split the defund ObamaCare language away from the bill that pays the government's bills. But they didn't have enough votes to pass it that way, in part because powerful outside groups like the Club for Growth and Heritage Action pushed GOP members to oppose it.

Their solution: Kick it to the Senate, where leaders felt Cruz and others were pressing for an impossible scenario.

That's why Cruz's comments -- and similar noises from Lee and Rubio -- prompted such a strong reaction in the House.

"(Sens) Cruz, Lee and Rubio are like the kids in high school who would yell fight, fight, fight, but have never thrown a punch in their entire life," a Senior GOP aide told NBC News after Cruz released his statement.

"I'm not surprised, but I'm not that impressed by those guys anyway," Rep Peter King, R-N.Y., told reporters. King has been open about his distaste with the far-right wing of the Republican caucus in the Senate, prompting him to say he's considering a run for President in 2016 to help balance the field.

House Republicans plan to pass their bill to fund the government (and defund Obamacare) as early as Friday of this week, likely with only Republican votes. The bill would keep the government funded at the current level of $986 billion until December 15th, a deadline that they hope to have appropriations bills completed. Current funding for the government would expire on September 30th if Congress fails to send legislation to the President's desk for his signature.

But in a sign that this debate may take Congress, yet again, to the brink of a fiscal deadline, House Majority Leader Eric Cantor, R-Va., announced Wednesday that the House has cancelled its scheduled recess for the week of September 23rd, and may be in during the weekend running up to the end of the month.