The partial agency shutdown, which began on July 23 and is likely to continue at least through Labor Day, has also idled tens of thousands of construction workers on airport projects around the country. Dozens of airport inspectors have been asked by the F.A.A. to work without pay and to charge their government travel expenses to their personal credit cards to keep airports operating safely.

Air traffic controllers and airplane inspectors, who are paid with separate accounts, have continued to work, but workers who oversee research on aviation systems, grants for airports and facilities and operations equipment have been furloughed.

If the stalemate continues through Labor Day, the government could lose roughly $1 billion in tax revenues on airline ticket sales.

Ray LaHood, the transporta-tion secretary, said he firmly believed that passenger safety was not at risk.

“No safety issues will be compromised,” Mr. LaHood told reporters on a conference call. “Flying is safe. Air traffic controllers are guiding airplanes. Safety inspectors are on duty and are doing their job. No one needs to worry about safety.”

The House began its August recess on Monday night, and the Senate followed Tuesday, leaving little hope for a resolution until Congress returns in September. President Obama, in remarks after the Senate’s passage of the debt ceiling bill, urged Congress to break the impasse, which he described as “another Washington-inflicted wound on America.”

The impasse centers on disagreements between Republicans and Democrats over a program that subsidizes commercial air service to rural airports. But behind the scenes, a larger fight has been taking place over federal rules on labor elections in the airline industry.

Randy Babbitt, the F.A.A. administrator, said in a conference call with reporters on Tuesday that the agency was depending on the “professionalism” of airport safety inspectors to continue their work without being paid, because their jobs are paid for with money that is awaiting Congressional authorization.

Those inspectors are the primary individuals responsible for ensuring that commercial airports comply with federal regulations. They also support runway safety action teams, oversee construction safety plans, investigate runway incursions and ensure that corrective action is taken on safety discrepancies.

“The reason they are out on the job is because of the risk to operational safety or life and property,” Mr. Babbitt said. “We can neither pay them nor can we compensate them for expenses. We are depending and living on their professionalism at this point.”

It is unclear how long the inspectors can continue to pay the bills for their own travel and hotel expenses. Typically, each of the roughly 40 regional inspectors travels to up to five airports in each two-week period, F.A.A. officials said.

When F.A.A. financing expired last month, the agency also lost the ability to collect taxes on airline tickets. Those taxes amount to about $30 million a day and are paid into a trust fund that pays for much of its operations.

The House passed a bill last month that would extend F.A.A. financing through Sept. 16 and allow it to continue collecting the ticket tax. Congress has passed 20 such temporary spending bills over the last four years, in part because it has been unable to agree on a larger, long-term authorization of the agency’s budget and capital plans.

But the House temporary bill also would end $14 million in subsidies that provided commercial airline service to 16 rural airports. The law was written in a way that appeared to single out for closing airports in the states of prominent Senate Democrats, including the majority leader, Harry Reid of Nevada.

Democrats say Republicans are trying to save a few million dollars at the expense of the ticket tax, which would generate roughly $200 million a week.

Some of the airport closings were included in a long-term spending bill passed by the Senate in February. But Senate Democrats, including Senator John D. Rockefeller IV of West Virginia who is chairman of the committee with jurisdiction over the F.A.A., objected to their inclusion in what they said should have been a “clean” temporary spending measure.

Robert Pear contributed reporting.

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