AP Photo/Charles Dharapak

ABC News' Mary Bruce and Alexandra Dukakis report:

President Obama and Republican senators had a "good exchange of ideas" this evening during their roughly two-hour-long dinner at the posh Jefferson Hotel, just blocks from the White House, according to a senior administration official.

Sen. John McCain, R-Ariz., gave the meeting a thumbs up as he exited the hotel, saying it was "just fine," "great" and "wonderful."

McCain told reporters gathered across the street that it was a "very enjoyable evening," but declined to discuss specifics.

Obama invited 12 GOP senators to break bread as part of a larger effort to jump start budget negotiations and try to cut a deal with rank-and-file Republicans.

"The president greatly enjoyed the dinner," the administration official said.

But did they make any progress?

"We'll see," Sen. Tom Coburn, R-Okla., told reporters. Sen. Pat Toomey, R-Pa., described it as a "good, constructive conversation."

"His goal is ours. We want to stop careening from crisis to crisis … solving every problem by meeting the crisis deadline," said Sen. Mike Johanns, R-Neb. "Today was a good step and we'll see what happens."

The extremely rare meeting has also fostered a new point of contention: Who picked up the tab?

According to the White House, President Obama paid for the meal out of his own pocket.

Sen. John Hoeven, R-N.D., however, claimed the bill was split.

And so it continues…

Here is a full list of attendees at tonight's dinner: Sen. Lindsey Graham, R-S.C.; Sen. Bob Corker, R-Tenn.; Sen. Kelly Ayotte, R-N.H.; Sen. John McCain, R-Ariz.; Sen. Dan Coats, R-Ind.; Sen. Tom Coburn, R-Okla.; Sen. Richard Burr, R-N.C.; Sen. Mike Johanns, R-Neb.; Sen. Pat Toomey, R-Pa.; Sen. Ron Johnson, R-Wis.; Sen. John Hoeven, R-N.D.; and Sen. Saxby Chambliss, R-Ga.