Shook added that lawmakers don't have far to go to do what she and other leaders are suggesting.
"The House has passed a bill, the Senate has passed a bill," she said. "All that's left is for the House to appoint conferees and them to be reconciled."
The negotiations have been held up since May, when the House passed a four-year, $59 billion funding bill for the FAA. The bill — which already differed from the two-year, $34 billion bill that the Senate passed in February — included a provision that nullifies rule changes from the National Mediation Board that make it easier for airline and railroad employees to join unions.
Democrats in the Senate objected strongly to the union provision, and President Obama threatened to veto the bill if the final version included it.
The fight preceded the shutdown of the FAA in August but was never far from the surface, as Democrats accused Republicans in the House of inserting poison pills into the funding routine as political retribution for their stance on the union issue.
Moak said the battle over union rules should be fought another day.
"The labor issue is one of many issues left to reconciled," he said in response to a question from The Hill. "It has no place in the FAA bill. We need to move on."
The August shutdown of the FAA is projected to have cost the federal government $30 million per day because the sales tax on airline tickets wasn't collected for 13 days.
Another issue dividing lawmakers is the number of long-distance flights at Reagan Airport. Federal law allows only 12 nonstop flights over 1,250 miles to and from the airport each day. Other long-distance flights to the Washington area land at Dulles Airport and Baltimore-Washington Airport (BWI), which are both about 30 miles from the District.
The version of the FAA bill approved by the Senate would increase the number of Reagan flights to 28, but the measure passed by the House would leave the number unchanged.
Despite there being so many unresolved issues between the chambers, Shook said the divide is not as wide as it seems.
"There's a gap between what happens in Washington, D.C. and the rest of the country," she said. "We're here today to shine a light on this issue for the rest of the country."
A Republican House staffer said the chamber was working on both the FAA issue and paying back workers who were furloughed earlier this month, but did not have a timetable for votes on those measures.
A Democratic congressional aide said a bill in the House would have to be unveiled by the end of the week to comply with the three-day review rule implemented by Republicans when they took over the chamber this year.
The current funding of the FAA expires Sept. 16.