Rep. Nick Rahall (D-W.Va.) said he shared Mica's optimism that deadline could be met.
"It’s not difficult,” Rahall said. “Anything that is unresolvable we will come back and do them ourselves … we are all in this together.”
Perhaps chief among the outstanding issues are provisions in the House version of the bill that would make it harder for transportation workers to unionize.
In a speech to the Washington Aero Club this week, Rockefeller said the provision was the result of "a fight between one single airline and organized labor." He accused Mica of making the union rules "paramount" to passing a long-term funding bill for the FAA, which has had 22 short-term extensions since 2007.
Heading into the meeting Tuesday, Rockefeller did not share Mica's confidence a deal could be reached before the short-term funding bill for the agency that was passed in September expires at the end of January.
"I'm having a meeting tomorrow with three people who should be getting together to work out problems, but we'll have almost nothing to say to each other," he said of the meeting Tuesday.
Earlier this year, the House and Senate each passed long-term authorization bills for the FAA last year, with the lower chamber approving a four-year, $59 billion measure for the beleaguered agency and the Senate passing a two-year, $34 billion bill.
—Hill reporter Erik Wasson contributed to this report.