Although there is no defined timeline, top Senate Democrats indicated on Monday that they believe the Federal Aviation Administration authorization bill will fly through the Senate under the new rules deal that minimizes filibusters and allows unlimited amendments.

"We have tried to get this bill through in the past but turbulence caused the bill to stall last year," Schumer said. "But we predict smooth skies ahead. We expect the bill to pass this week with strong bipartisan support."

Senate Majority Leader Harry Reid (D-Nev.), who controls process on the Senate floor, said he believes the handshake agreement between the parties should help expedite passage if Republicans limit their amendments to the bill's subject matter.

"I hope we don't have hundreds and hundreds of amendments on this; I hope we stick the subject matter," Reid said. "This is an open amendment process. We are going to try to have the Senate start being the Senate again. We are going work our way through this as quickly as we can with no defined timeline on it."

Sen. Jay Rockefeller (D-W.Va), the bill's sponsor, said he expects a much "quicker, saner, process."