Congress yesterday resolved its latest abortion dispute and approved temporary financing for the federal government, although the bureaucracy had to muddle through a day without any spending authority.

Within minutes after convening, the House, without debate or a recorded note, accepted a Senate compromise on abortion funding and whisked the huge stopgap spending resolution off to President Carter, who signed it later in the day.

The resolution means that the government can continue to spend money at current or slightly higher rates through Dec. 15, when Congress presumably will have acted on regular appropriations bills that are currently in a preelection deepfreeze. In the mieantime, Congress can go home and campaign.

By failing to adopt the measure before yesterday's start of the new fiscal year, Congress technically left the bureaucracy with its money spigots turned off. But it was basically business-as-usual downtown, even though workers were theoretically at their desks only to wind down their operations.

Noting that Congress had put the bureaucracy through similar financial wringers in the past, although never such a big one, House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) observed before the House vote that someone "always blinks and the government proceeds."

While comments from agency officials indicated some work interruptions and long coffee breaks, the government's day in limbo seemed to have no serious effect on important operations. Managers from several departments did, however, spend the day planning to call traveling bureaucrats back home and compiling lists of people who would have to be furloughed.

"We sure wasted a lot of time and energy in this exercise," one major department budget official said. A spokesman for the Office of Management and Budget said the executive branch had no estimate of what all the contingency planning cost.

Only the federal judiciary seems to have a clear shot at coming out a winner in the affair. Because the continuing resolution's cap on judges' pay didn't pass in time, more than 800 federal jurists may be eligible for a 9.1 percent pay raise.

Congress is likely to argue, as it has in the past, that the wage freeze is retroactive to Tuesday midnight. But the issue is now before the Supreme Court, because judges sued when Congress withheld similar raises, arguing that the Constitution prohibits reducing a judge's salary.

At issue in 18 hours of conferences and floor squabbles in Congress Tuesday and on into yesterday morning was an anti-abortion rider to the funding bill that proposed to discontinue Medicaid funding of abortions for poor women in cases of rape or incest. The House wanted the new restriction; the Senate didn't.

The compromise, proposed by the Senate in a post-midnight session after the House had gone home, permits a woman to get a Medicaid-paid abortion after rape as long as she reports the offense within 72 hours, rather than the present 60 days. No reporting deadline is required for incest.

The Senate proposed the compromise in place of a recommendation from House-Senate conferees, which the House approved, 292 to 100, for a 48-hour reporting deadline for both rape and incest.

The whole episode, which Sen. Patrick J. Leahy (D-Vt.) said made Congress look "like a bunch of idiots," underscores the trouble into which Congress can get itself and others when it delays regular money bills and has to resort to stopgap funding with deadlines.

It also points up once again the potency of the abortion issue, especially on the House, with its biennial elections and its vulnerability to single-issue constituencies.

Under the right combination of circumstances, the whole government can be held hostage to these pressures, as was illustrated in this week's showdown, even though it may not be as easy to shut down or even hobble the bureaucracy as some might wish.

"If it isn't abortion, said Speaker O'Neill, "it will always be something."

Nonetheless, the ability of the government of muddle through became evident in a variety of ways:

The Pentagon rose above it all by issuance of a directive from Defense Secretary Harold Brown for employes to proceed in a "prudent" manner on the assumption that Congress would act soon.

The Justice Department responded to callers to its public affairs office with a prepared statement to the effect that only questions involving protection of life and property or agency shutdown could be answered for the time being.

At the Agriculture Department, Tom Sand, press secretary to Secretary Bob Bergland, was quoted by United Press International as saying, "Nobody's doing anything -- business as usual."