The House last night gave speedy, overwhelming approval to a stripped-down stopgap spending bill to keep all the government operating after existing funding authority runs out Friday at the end of the current fiscal year.

The "continuing resolution," which would fund most government agencies at levels somewhat higher than current spending through Nov. 15, was approved 261 to 160. The Senate is expected to act on its version of the legislation today.

The ease with which the House approved the normally trouble-plagued stopgap resolution, coupled with Senate Appropriations Committee approval yesterday of a similarly restrained measure, raised hopes that Congress could mark the start of a new fiscal year without its normal deadline-defying chaos.

During brief debate on the measure, Rep. Silvio O. Conte (R-Mass.), ranking Republican on the House Appropriations Committee, praised his colleagues for keeping the bill "from being a Christmas tree or at least a Thanksgiving turkey."

Congressional leaders said that, if the Senate acts with dispatch, the measure is expected to be signed by President Reagan in time to avoid any disruption in government activity. But, in refusing to consider requests for assorted spending proposals, including a $1.5 billion add-on for social welfare programs already authorized by the House, Congress appeared assured of continuing battles over domestic spending for fiscal 1984.

There was talk yesterday, for instance, of loading up a supplemental appropriations bill already on track for congressional action with all the spending plums that got left out of the continuing resolution and the regular appropriations bills making their way through Congress.

The stopgap measure is needed because only four of the regular 13 appropriations bills for next year have been enacted. There are prospects for final passage of only two others by Friday's deadline. The bill, in effect, provides interim spending authority for unfunded departments and agencies until Nov. 15 or until their regular bills are passed.

Without such stopgap funding, agencies and departments that have not received their regular appropriation from Congress face at least technical shutdowns after the start of a new fiscal year.

There were also problems for the domestic spending add-on in the Republican-controlled Senate.

As of late yesterday, Senate Labor and Human Resources Committee Chairman Orrin G. Hatch (R-Utah) was refusing to hold a House-Senate conference on the bill until two prospective Republican conferees, Sen. Lowell P. Weicker Jr. (R-Conn.) and Sen. Robert T. Stafford (R-Vt.), agree to oppose the higher authorization proposed by the House. But Weicker and Stafford were refusing to make such a commitment.

Held hostage is a vocational rehabilitation bill that the House used as a vehicle for the spending add-backs. As passed in different forms by the House and Senate, it would extend current programs, for which existing authorization runs out Sept. 30, and add some new programs.

Yesterday Democrats on Hatch's committee, joined by Weicker and some other Republicans, were preparing to ask Senate Majority Leader Howard H. Baker Jr. (R-Tenn.) to appoint conferees if Hatch won't.

In Senate action on the continuing resolution, meanwhile, the Appropriations Committee as usual substituted its proposed spending levels for those of the House. The Senate committee approved a defense spending level of $253 billion, as opposed to $228 billion proposed by the House.