By Stephen Collinson

CNN

WASHINGTON (CNN) -- The GOP turned into the Grouchy Old Party, as recriminations flew after the failure this week to repeal and replace Obamacare -- the greatest motivating cause of Republican voters for more than seven years.

Soon after Senate Majority Leader Mitch McConnell admitted defeat Tuesday in his bid to jam the bill through the Senate, President Donald Trump, different factions on Capitol Hill and outside conservative activists started assigning fault for the legislation's collapse.

Trump, facing criticism of his own conduct in the failed effort to replace his successor's signature law, suggested simply that the Republican majority on Capitol Hill was not up to the job.

"For seven years, I've been hearing repeal and replace from Congress, and I've been hearing it loud and strong," Trump said at the White House. "And then when we finally get a chance to repeal and replace, they don't take advantage of it."

Meet the 53 angriest people in town. One President who wants to sign something that repeals Obamacare, and 52 Republican senators who can't agree on how to advance health care legislation without tearing the GOP apart.

Republicans will have a chance to air their frustrations Wednesday as all GOP senators have been invited to 1600 Pennsylvania Avenue for lunch, a White House official told CNN. Discussing health care is on the menu, and given the way lawmakers were speaking Tuesday, expect some blame to be doled out as well.

The anger in Washington is acute, not just because overturning Obamacare has become a holy grail for Republicans, but also because six months into the Trump era, while operating a monopoly on power on Capitol Hill, the party has yet to pass a landmark piece of legislation.

As is often the case in a blame game, each key player in the argument was seeking to protect their own political interests, in the expectation that a backlash from Republican voters is likely after Tuesday's drama.

The defeat of McConnell's initiative, raised questions not just over the future of American health care, but the cohesion of the Republican majority itself, as the GOP, united in opposition, finds it tougher to be a credible governing force.

For years, hopes of repealing the Affordable Care Act have kept a fractious party united in Washington. Now, with responsibility for Americans' health care coverage resting solely with Republican lawmakers that is no longer the case and Trump and McConnell could not even secure 50 votes in the Senate for the repeal and replace bill.

Amid rising GOP recriminations, Trump tweeted that he had been let down by "all of the Democrats and a few Republicans. Most Republicans were loyal, terrific & worked really hard."

His use of the word "loyal" was intriguing, since it suggested he believes that despite his own diminished approval ratings and departures from Republican Party orthodoxy, his is owed unquestioning support as a matter of course by members of his own party.

But Trump also said his party won't own the result.

"I think we're probably in that position where we'll just let Obamacare fail. We're not going to own it. I'm not going to own it, I can tell you. The Republicans are not going to own it. We'll let Obamacare fail and then the Democrats are going to come to us and they're going to say "how do we fix it, how do we fix it," or "how do we come up with a new plan."

While the White House made an attempt to hammer Democrats for refusing to help in repealing the centerpiece of their last President's legacy, other White House officials also turned their fire on GOP lawmakers.

"Congress needs to do their job, and they need to do it as quickly as they can," White House deputy spokeswoman Sarah Huckabee Sanders said Tuesday.

McConnell is now digesting the damage to his reputation as a master Senate strategist, and appeared keen make members of his own caucus pay a price for their defiance. The majority leader said he will set procedural vote on a full repeal of Obamacare -- with a replacement to be organized some way down the road -- for next week.

It's a vote many Republican senators already made in 2015 -- but with the safety net of a certain Obama veto. Messaging bills, Republicans have learned, are much easier to pass.

The measure has the potential to put lawmakers in a tough political spot if they go against the wishes of the wider GOP base. But it does have the virtue of allowing others to say they did actually vote to repeal Obamcare.

Even so, at least four senators have already said they will vote against the motion, more than the number of GOP dissidents needed to stop it passing.

Frustration about their political plight bubbled to the surface of the weekly GOP lawmakers policy lunch. One Republican source briefed on the events inside said that "senators are upset" and that was clear in the meeting.

But the source said there were so many different GOP factions that not all of the ire was directed at McConnell over his handling of the bill.

The source also said that there were no signs in the room that McConnell could face a challenge to his leadership post over the episode.

Backlash?

Outside Washington, the great unknown is how much backlash senators will face for their failure to live up to a long-held Republican promise.

CNN's Eric Bradner reported Monday that Trump and other White House officials have had conversations with prospective GOP candidates about challenging Arizona Sen. Jeff Flake, who is up for re-election next year, and has long feuded with the President.

One candidate who is already running a primary campaign against Flake used the Obamacare repeal collapse to take a shot at the Arizona senator.

"Jeff Flake needs to start doing his job and stop lying to the Arizona voters about his position on #Obamacare. He voted for full repeal in 2015 as a show vote, a ruse, a lie," Kelli Ward wrote on her Facebook page.

Flake may not be the only person feeling the heat.

Ken Cuccinelli, head of the Senate Conservatives Fund vowed to target Republican Senators who he said had no excuse not to repeal Obamacare with a GOP President in the White House.

"Working with the grassroots across the country, we will seek to identify, recruit, and fund conservative challengers against Republican senators who vote against repeal," Cuccinelli said.

"If they won't keep their word and if they can't find the courage to repeal a liberal takeover of our health care system that has hurt so many American families, they should be replaced by someone who will."

CNN's Dan Merica, Eric Bradner and Ted Barrett contributed to this story.