WASHINGTON — President Obama on Tuesday painted a dire picture of federal government operations across the United States should automatic budget cuts hit on March 1: F.B.I. agents furloughed, criminals released, flights delayed, teachers and police officers laid off and parents frantic to find a place for children locked out of day care centers.

“Federal prosecutors will have to close cases and let criminals go,” Mr. Obama said, flanked by law enforcement officers at the White House. “Tens of thousands of parents will have to scramble to find child care for their kids.”

While the effects may ultimately be significant, many are unlikely to be felt immediately, officials said Tuesday after the president’s remarks. Rather, they will ripple gradually across the federal government as agencies come to grips in the months ahead with across-the-board cuts to all their programs.

Administration officials insisted that government contractors and state governments will begin receiving word quickly about programs that must be reduced or terminated. The Defense Department is planning to give notice to 800,000 civilian workers on Wednesday that furloughs might be necessary if the automatic cuts go into effect.