Republican Senators returned to the Capitol today after a meeting with President Obama that one senator described as "good" but "inconclusive."

Sen. Susan Collins, R-Maine, who has sketched out an alternative to the framework presented by the House GOP, said she was able to discuss her plan with the president, but he declined to endorse either proposal.

"The president listened carefully. He said that some of the elements were issues we could work on but he certainly did not endorse," Collins told reporters as she returned to the Capitol. "It was a good exchange but it was an inconclusive exchange."

"He clearly wants the government to be reopened and he clearly wants at least an extension of the debt limit," she added.

The plan crafted by Collins and several Republican senators would re-open the government and extend the debt ceiling until at least January 2014. The proposal also repeals the medical device tax, introduces more flexibility for managers to deal with sequestration, and requires income verification for the insurance exchanges.

Collins said the meeting signaled "progress" to the extent that President Obama is now sitting down with members of Congress to find a solution to the budget impasse.

"He has sent somewhat conflicting signals about what length of a debt ceiling increase he would accept and what might be attached to it or what might not be, but at least he's talking to members of Congress on both sides of the aisle," Collins said. "He may not want to call it a negotiation. That's what I would call it and I do view that as progress."

"I think it's imperative that we act with speed. I'm pleased that the president is now finally engaged," she added.

But Sen. John Cornyn, R-Texas, said the meeting, which lasted about 90 minutes in the State Dining Room, amounted to another "predictable lecture" from the president.

"I think it was more a sign that there were a lot of long-winded people, senators included," Cornyn said.

Asked whether the president signaled an openness to entitlement reform, or tweaking the Affordable Care Act, Sen. Jeff Flake the president listened but was non-committal.

"He said individual things that can improve the act, not gut it, that he'd look at it," Flake, R-Ariz., said. "There was much said, but no definitive answer there. That was a bit frustrating on our part."

After the meeting at the White House, Senate Republicans met for a private lunch in the U.S. Capitol to discuss their strategy moving forward.

"I think we had a very useful meeting with the president. He spent a lot of time with us, and interacted with our members and now we're back here to actually work on trying to get a solution on a bipartisan basis," Senate Minority Leader Mitch McConnell said. "Hopefully we can find a way forward."