Spurred by the belated realization that the Democratic Party may have fumbled away a once-in-a-decade opportunity, political operatives in the White House are searching for ways to restore political patronage to tens of thousands of jobs in the Census Bureau.

The jobs, temporary positions for "enumerators" who help gather and collate data during the decennial census, have traditionally been distributed by the party holding the White House as a plum for loyal followers and a lure to attract new party workers.

Dispensing the jobs is a cherished prerogative for local party captains -- particularly when the census year coincides with a presidential election, as it will in 1980.

But the Carter administration discovered recently that its own Civil Service "reform" legislation, which Congress passed last year, apparently rendered this old political tradition illegal. The act requires merit system hiring for most federal jobs, and, though the Census jobs are not specifically mentioned, they are not specifically excluded, either.

Accordingly, officials at the Census Bureau and its parent agency, the Commerce Department, are designing a new, nonpartisan hiring practice to staff the 1980 census. But, at the same time, the White House has been studying possible steps to preserve the patronage boon.

On the surface, this problem would appear to be no problem, because the statute gives the president authority to exempt classes of employes from the merit requirement.

The White House is reluctant to use that power, however, because it might appear that Carter were subverting a statute he forcefully supported. "When this was discussed, everyone got post-Watergate fever," explained Carolyn Jefferson of the Commerce Department.

Another possibility, according to a White House political adviser, is to forge ahead with patronage hiring in the hope that a legal challenge would take so long that the work would be finished before the case was decided. But that option, too, seems unlikely, because it, too, creates the image of a president undermining his own "reform."

The most likely course appears to be an appeal to Congress to pass a new bill making it clear that temporary census enumerators are not subject to merit hiring. The administration has been sounding out congressional leaders on that approach, which would eliminate any uncertainity about the jobs and pass the responsibility for this political action from the White House to Capitol Hill.

To their delight, administration officials received a sympathetic reply from one of the Republican Party's chief spokesmen on Civil Service matters.

"I told them I'd go along with a bill to exempt those jobs," said Rep. Edward J. Derwinski (R-Ill.), the ranking minority member of the House Post Office and Civil Service Committee.

"It wasn't our intent to cover those temporary census appointments," Derwinski said. "Anyway, we got to use those plums in '60 and '70, so it's only fair that we let the Democrats have them now.

"Some Republicans will probably fight an exemption like that," Derwinski went on. "That would be both normal and futile. The Democrats have enough votes to roll this thing right through if they want it."

The apparent inclusion of the Census jobs in the Civil Service law escaped the notice of officials on every level, including Carter.

Last summer the president personally recruited a veteran Democratic activist to oversee the distribution of the 1980 jobs. When the president's choice, Patti Knox of Detroit, arrived here to start work, she read the new statute and concluded that the job she was hired for had been rendered illegal.