Senate Majority Leader Harry Reid (D-Nev.) on Sunday said he exited a meeting with the president and the chamber's Democratic caucus ready to tackle the more critical parts of the healthcare debate.

"President Obama has been a senator, and he understands the process that we're going through now. In short, he pledged to working with us in any meaningful way he can," Reid said at a press conference this afternoon.

"There are still a few things we need to work out in the bill, and the issues are being narrowed as we speak," the majority leader added, noting that Democrats had so far made "great progress" on reform.

Some of those remaining, contested topics could actually see debate next week.

Sen. Ben Nelson (D-Neb.) will introduce an abortion amendment on Monday, Reid announced this afternoon. Meanwhile, a team of five moderates and five progressives continue to forge ahead with negotiations on the "issues they care about" in the healthcare bill, the majority leader added.

But while Reid praised the president's visit, reiterating the party's committment to passing a reform bill, Senate Republicans continued debating that proposal on the Senate floor.

Most in attendance, including Sen. John McCain (R-Ariz.), lambasted their Democratic colleagues for again holding a meeting behind closed doors, away from the cameras of C-SPAN.

"I think we're all ready to have a meeting with him," McCain added from the floor. "That was, as I recall on the campaign, that was going to be the change in Washington, we're all going to sit down, Republicans and Democrats."

"And I think on this Sunday afternoon we're all available...," he quipped, noting the rather unprecedented nature of a Sunday session of the Senate.