President Obama drew the line Tuesday on the budget stalemate, "[M]y understanding is the speaker and leader Reid are going to have a meeting [Tuesday afternoon]. If that issue does not get resolved and we don't start seeing progress, I want a meeting again [Wednesday] here at the White House."

Indeed, House Speaker John Boehner (R-Ohio) and Senate Majority Leader Harry Reid (D-Nevada) did hold talks. Afterwards, their staffers put out identical statements, noting the two had "sat down privately and had a productive discussion" and "agreed to continue working on a budget solution."

Still, no compromise was announced on how to fund the government for the rest of this fiscal year. So, would the president summon the leaders back to the White House?

Late Tuesday, the White House was still watching developments. A senior administration official tells Fox that Capitol Hill staff continued to meet throughout the evening. "We'll see how they progress - and if there's a need to meet at the White House, then that's something we'll announce in the [morning]," the official said.

Lining up schedules Wednesday could prove difficult as Israeli President Shimon Peres is making the rounds on Capitol Hill and President Obama is headed to Pennsylvania for an energy event.

But the president was clear what would happen should an impasse persist, "I will invite the same folks that we invited today. And if that doesn't work, we'll invite them again the day after that. And I will have my entire team available to work through the details of getting a deal done."