Prodded by warnings that congressional dawdling might slow the federal bureaucracy to a halt by the middle of next week, the Senate moved sluggishly yesterday toward approval of stopgap financing for most of the government.

When it failed to finish by late afternoon, the Senate put off action until Monday, leaving only a day or two before the congressional recess in which to resolve House-Senate differances.

The emergency financing plan, a version of which has passed the House, would expire Dec. 15, requiring Congress to come back after the Nov. 4 elections to finish its appropriations work or to pass another so-called continuing resolution.

Yesterday the Senate voted to cut $550 million from the $1.3 billion that the House approved for anti-recession public jobs, while adding $200 million for youth employment.

The cut, which resulted from a compromise between supporters of the jobs program and senators who wanted even heavier cutbacks, would bring the program more in line with job levels anticipated by spending targets that Congress already has approved for fiscal 1981.

A $900 million cut, proposed by Sen. Lawton Chiles (D-Fla.) along with the $200 million outlay for youth jobs, drew heavy fire from Sen. Daniel Patrick Moynihan (D-N.Y.), who accused the Senate's Democratic majority of "dismantling our own programs . . . ripping apart what is left of John F. Kennedy's legacy."

The continuing resolution is required because Congress is even more laggared than usual in passing appropriations bills in advance of the Sept. 30 end of fiscal 1980. It has yet to complete action on any money bills for fiscal 1981.

Without a continuing resolution, the major departments of government -- including a Pentagon as well as the big domestic agencies -- would be barred as of Oct. 1 from spending any money except for orderly shutdown of their operations.

If Congress fails to act by midnight Tuesday "the whole government will stop operating . . . nobody should go to work Wednesday morning," Senate Appropriations Committee Chairman Warren G. Magnuson (D-Wash.) warned as leaders of both parties urged senators to restrain themselves in proposing time-consuming amendments.

There are major differences between the House resolution and the measure proposed by the Senate Appropriations Committee, so after the Senate finishes, a conference will be required to iron out differences.

The House measure proposed spending at 1981 level anticipated by either House or Senate appropriations bills, whichever is lower. The Senate committee resolution would have some agencies spending at 1980 levels, although there are major exceptions, including the Pentagon, which would be allowed to spend at the 1981 level proposed by the House. This amounts to $20 billion more for defense on an annual basis.

Appropriations delays in the past have caused Congress to put large chunks of the bureaucracy on stopgap funding, but never virtually the whole government.Moreover, the shutdown rules are more stringent this year because an attorney general's ruling, drafted during an earlier funding dispute over the Federal Trade Commission, prevents agencies from continuing to spend money after a cutoff date on the implied promise of eventual congressional financing.