Though planes continued to fly unhindered nationwide, a dispute about service to a handful of tiny airports crippled Federal Aviation Administration operations for the third day Monday, costing the agency an estimated $30 million a day.

With House Republicans and Senate Democrats apparently in locked positions, and compromise an elusive pursuit on Capitol Hill this month, no one was ready to predict when funding might be restored to the federal agency.

“Don’t hold your breath,” advised one Senate staff member, who spoke on the condition of anonymity.

Senate Commerce Chairman John D. Rockefeller IV  (D-W.Va.) late Monday called on the House to meet with its Senate counterparts Wednesday to work on resolution of the disagreement.

House Transportation Chairman John L. Mica (R-Fla.) responded that the Senate should instead adopt a House plan.

More than 4,000 FAA staff members, including about 1,000 in the Washington region, were furloughed when a stop-gap funding extension expired at midnight Friday. Construction projects at several airports across the country were halted.

Congress has extended FAA funding 20 times since its last long-term funding authorization expired in September 2007. Last week, when the House approved its version of the 21st extension, it included a provision curtailing subsidies for flights to several small airports. The Senate balked at that provision, joining the Obama administration in demanding a “clean” extension bill.

“The fact that Congress can’t work this out is exactly why the American people are fed up with Washington,” Transportation Secretary Ray LaHood said Monday. “There’s no excuse for Congress failing to pass a clean FAA bill, the way they have done on 20 other occasions.”

The House showed no inclination Monday to produce such a bill, and the Senate did not move to send a provision-free extension bill over for House approval.

“Secretary LaHood keeps saying Congress has to pass a clean extension,” said a House Transportation Committee staff member, who spoke on the condition of anonymity. “It doesn’t. Congress simply has to pass an extension. Also, he keeps saying Congress has passed a clean extension 20 times already. Not every previous extension was clean.”

The 15th House extension was sent to the Senate last year with a series of provisions regarding pilot fatigue and aviation safety.

The provisions in the current House bill reflect an as yet unresolved issue in long-term FAA funding bills passed by the House and Senate this year. There is disagreement over the future of the Essential Air Service system, a program that subsidizes commercial air service to small airports mostly in rural regions. EAS was launched with airline deregulation in 1978 as a 10-year effort to ensure service to those airports while establishing their commercial viability. Its life span has been extended by Congress ever since, its cost growing from $7 million a year in 1978 to $163 million today.

The Senate reauthorization bill eliminates EAS funding for 10 airports that are within a 90-mile drive of a larger airport. The House bill would eliminate the program everywhere but in Alaska and Hawaii by Oct. 1, 2013.

With House and Senate staff members trying to iron out those and other differences between the two bills, Mica inserted a provision in the House funding extension to eliminate service to three other airports.

The three, with their federal per-passenger subsidies, are: Ely, Nev. ($3,720), Alamogordo/Holloman Air Force Base, N.M. ($1,563) and Glendive, Mont. ($1,358).

“If the Senate cannot agree to a simple provision, which it approved earlier this year, to eliminate excessive subsidies between $1,358 and $3,720 per ticket at three airports, then we don’t need to convene a conference meeting,” Mica said.

“I know this is an important issue to the many rural airports, but it shouldn’t put the whole FAA into a furlough position,” Sen. Mark R. Warner (D-Va.) said Monday. “When you’re holding hostage the traveling public, when you hold hostage thousands of folks who are just trying to do their job, I think that’s bad policy and bad politics.

“You’ve got to have a willingness on both sides to make some compromise,” Warner said. “At some point, people continue to lose confidence in our government’s ability to do its basic job.”

Warner said one of the projects halted Monday was the construction of a $24 million air traffic control center in Warrenton.

The expiration of the FAA funding extension has proved a windfall for many of the nation’s airlines. It meant they no longer had to collect the federal per-ticket tax of 7.5 percent on airline travel. Rather than reduce ticket prices to reflect that, many airlines pocketed the money that normally gets sent to Washington.

Only a few airlines — Alaska Airlines, Frontier Airlines and Virgin America — said they would pass on savings to passengers.

FAA Administrator J. Randolph Babbitt said that stopping the flow of those tax revenues to the Aviation Trust Fund was like drawing checks on a checking account that has no new money coming in.

“The problem we have right now is that [Aviation Trust Fund] deposits just stopped,” Babbitt said. “That trust fund gathers about $10 billion annually, so this is a substantial stop to revenue.”