"We came from that meeting with a renewed commitment to keep working, to keep negotiating, and to get to yes," said Sen. Ted Cruz (R-TX).
"In my view, failure is not an option," Cruz told reporters outside the U.S. Capitol.
At the White House, the President had made a similar appeal.
"We should hammer this out and get it done," the President told Senators over lunch, as he said lawmakers should not leave town for their August vacation until that job is finished, and a bill is signed into law.
"The people of this country need more than a repeal - they need a repeal and a replace," Mr. Trump said.
The President's remarks were a notable turnaround from a day before, when he said Republicans should just let the Obama health law fail on its own; earlier in the week, he had suggested simply repealing the law, and waiting on a replacement.
"I would say there is no question the meeting gave a boost to the effort," on health care, said Sen. Bob Corker (R-TN). "I just hope we get over the line."
"He feels like we're very close to getting there," Corker said of the President, as the Tennessee Republican downplayed the President's latest shift on what he wants out of the Congress on health care.
A group of Senators were set to meet tonight at the Capitol to go over problems they had with some of the details, and to find a way forward.
"I think we are substantially there," said Sen. Bill Cassidy (R-LA), though he acknowledged there are obviously differences. "They are key."
"The President very much emphasized that there has to be a replace with the repeal," Cassidy added.
After the meeting, the Senate Majority Leader told reporters that he still plans to go ahead with a procedural vote next week on the Senate floor, to officially begin debate on the health care issue.
"We had a really good meeting with the President," McConnell said as he returned to the Capitol.
Whether that can bridge the gaps and thread the needle for Senate Republicans remains the big question.
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