As lawmakers trooped out of the U.S. Capitol on Thursday and headed home until early June, Senate Republicans told reporters they were making progress, but were still nowhere near finalizing a deal on a major overhaul of the Obama health law.

"Doing nothing is not an option," said Sen. John Cornyn (R-TX), as top Republicans tried to project a feeling that the GOP is making some headway in making changes to a bill approved in the House earlier this month.

"I believe Senators across the ideological spectrum are proceeding in good faith," said Sen. Ted Cruz (R-TX).

"Leader McConnell is doing a great job right now, focusing on the priorities that we've all agreed to, that are broken under Obamacare," said Sen. David Perdue (R-GA), who said he thought there would be legislative language put together in the near future by GOP Senators.

But one thing no one was talking about on the GOP side, was when a health care bill might get to the Senate floor for an actual debate, and vote.

"We're a long ways from that," said Sen. Mike Rounds (R-ND), "but you've got to start with something to begin with. And that's what this is all about."

But the schedule is already squeezing Republicans, as there are four work weeks in June, plus three in July - then Congress is scheduled to leave for a five week summer break that lasts until Labor Day.

If you are counting - that's 28 scheduled legislative work days between now and Labor Day.

Not only are there few work days, but Republicans still have to get the House bill past the scrutiny of the Senate Parliamentarian, and then make sure any changes also pass muster with strict Senate rules governing budget reconciliation, which prevents a bill from being subject to a 60 vote filibuster.

One item from the House bill that could be in trouble in the Senate, is the idea of allowing states to opt out of certain requirements from the Obama health law, like the list of "Essential Health Benefits" that must be covered by insurance.

How Republicans might broker some of the differences wasn't clear as members headed for the airport, though individual Senators are clearly looking for a breakthrough.

"Can you talk to me in two weeks? We're working on something," Sen. Bill Cassidy (R-LA) told reporters, refusing to give any hints of what he is trying to cobble together on coverage.

"No, cause I don't know if it works. I'm running it by actuaries, I'm running it by people who really know their stuff," Cassidy added.

And that's where Republicans are right now - still searching for a deal, while the clock keeps ticking.