White House: Trump not giving up on overhaul of Obama health law

"We're at the beginning of a process. I don't think we've seen the end of health care," Spicer added, labeling the Obama health law, "an abysmal failure."

Spicer said the White House is currently going through a post-mortem on what went right and what wrong in their effort, as he said members of both parties in Congress had already reached out to both the White House and Mr. Trump about finding some common ground on health care policy.

On Capitol Hill, both parties were still sifting through the embers of the GOP health care bill, which was yanked off the House floor on Friday afternoon before a final vote, clearly short on support, as it divided Republicans along several fault lines.

For many GOP lawmakers, the idea of giving up after just 18 days of work on health care changes, was not an option.

"We cannot walk away now, without even a vote," said Rep. Luke Messer (R-IN), a junior member of the House GOP leadership, said on the House floor.

"I will continue to fight for a conservative bill to repeal Obamacare and rebuild a people-first health care system," said Rep. Richard Hudson (R-NC).

There was no immediate signal on whether the White House or GOP leaders in Congress would look to tinker with the failed health bill of last week, or maybe start to develop a new plan.

But there were still clearly bruised feelings among Republicans in the House, with some taking aim again at members of the House Freedom Caucus, who stiff-armed the President's repeated requests for support.

"I'm angry about that," said Rep. Ted Poe (R-TX), who this weekend quit the Freedom Caucus, saying he's not sure the Freedom Caucus would vote for the Ten Commandments.

As for the Freedom Caucus, the President on Monday night was once more going after those more conservative Republicans in Congress, taking to Twitter for a second straight day to reprimand the group for not supporting the GOP bill.

Mr. Trump predicted that Democrats would come around and negotiate with him on health care changes, "as soon as ObamaCare folds," he wrote on Twitter.