Republican lawmakers say they expect President Reagan to sign legislation that rushes $672 million to the Veterans Administration, the federal prison system and an assortment of other programs said to need the money.

The House approved the supplemental spending bill by a 270-32 tally late Thursday, then sent the measure to the Senate, where it passed on a voice vote and was sent to the White House.Lawmakers prided themselves on fighting off temptation and refraining from the frequent practice of attaching pet projects to the measure, saying they abided by a pact congressional leaders reached with Reagan last fall. The legislation was labeled a "dire emergency" bill because the measure was supposed to be limited to that type of spending.

House Majority Leader Thomas Foley, D-Wash., said it was "a very stringently conceived bill that is absolutely required for the continuation of many essential services."

The $672 million bill was a compromise between a $189 million measure approved by the House on July 27 and a $633 million version passed by the Senate on Wednesday. The bill is for the 1988 fiscal year, which ends Sept. 30. In addition to the fresh money, the bill would allow $200 million to be transferred among the budgets of various agencies.

Eyeing a nearly monthlong recess that began at the close of the day's business, conference committee members worked out the compromise and rushed the bill through final approval in both houses in a single day.

The few objections in the House came from legislators who complained this measure was no different from other spending bills. "This is no emergency," said Rep. Bill Frenzel, R-Minn.

As often happens with spending bills in Congress, the deal was reached by each chamber agreeing to most of what the other had proposed, rather than mutually chopping away at each other's sought-after projects.

Thus, the House accepted Senate provisions that would give the Veterans Administration $530 million in new spending to help pay for an increase in some benefits, a burgeoning caseload and medical care.

The Senate also had sought $23 million to help the FBI keep an eye on Soviet inspectors monitoring American compliance with the new nuclear arms treaty. The final bill contained $14 million of that amount.

The Senate consented to spending $15 million for state unemployment programs - the House had wanted $50 million - and $24 million the House wanted so the government can process refugees from the Soviet Union, Eastern Europe and elsewhere.

In addition, the measure bore $75 million for the Department of Justice, mostly for expenses arising from last year's rioting by Cuban detainees in prisons in Atlanta and Oakdale, La.

It also had $60 million to help the Coast Guard keep its patrols going; $55 million for the Agriculture Department to pay for some drought costs; $49 million for benefits to people who lose their jobs because of foreign competition, and $43 million for payments to people with black lung disease.