WASHINGTON — After dealing with the debt crisis, Senate negotiators tried and failed on Tuesday to end a stalemate over temporary financing for the Federal Aviation Administration, leaving 4,000 agency employees out of work and relying on airport safety inspectors to continue working without pay.

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.