In the midst of the Carter campaign's furious efforts last month to line up votes for the Iowa caucuses, Mike Blouin had a little campaign of his own going.

The 34-year-old ex-congressman from Dubuque, who was defeated in 1978, let it be known on Capitol Hill and elsewhere that he was through with his old job of watching over piles of classified paper at the General Services Administration. What he wanted, he said, was a piece of the latest bureaucratic action in Washington -- the new Department of Education.

So while Blouin canvassed his old district for caucus votes for Carter, the wheels were in motion here for the Mike Blouin for assistant Secretary for vocational and adult education campaign.

Blouin delivered copies of his resume for the $52,750-per-year assistant secretaryship to the White House personnel office and to the still-shapeless Education Department -- including on them a mention of his experience as a fifth-grade teacher back in Dubuque. He buttonholed friends on the Hill and among the education associations to put in a good word for him and managed to wangle a short interview with brand new Education Secretary Shirley M. Hufstedler.

There even was a vague rumor floating around that placing Blouin in Education could help place Carter in the lead in Iowa.

As it turned out the Carter campaign did just fine in ex-congressman Blouin's home state and Blouin's resumes went into the hopper here along with some 2,000 others seeking jobs in the government's newest cabinet-level department.

The remainder of the jobs in the new department are likely to be filled from existing slots in the Department of Health, Education and Welfare and other Cabinet departments which handle bits and pieces of federal education chores.

In fact, Hufstedler still must wrestle with a promise made by President Carter to cut 500 jobs off the federal education job rolls. Some of those cuts will come from attrition, Hufstedler said recently, but she said she has not yet figured out how to meet the full cutback promise.

Blouin now canvassing the Maine coast for Carter votes, concedes his quest for the assistant secretary job has shifted into a lower key.

"I think I'm still being considered though," he said yesterday.

Another job-seeker from North Carolina, showed up recently on the doorstep of Sen. Robert Morgan (D-N.C.) and was politely referred to the White House employment office for a proforma interview. After his pitch to a staff member, the man jubilantly returned to North Carolina and announced the local press that he had talked to the White House and had the job in his hip pocket.

It is clear that the appearance on the scene here of a new department Hufstedler's department officially begins operating -- the deadline is June 3 -- there will be some 17,000 jobs below the secretary on the organization chart.

But the stack of applications has Education Department officials somewhat puzzled.

"Technically," said one official yesterday, "we have just 10 openings for the new assistant secretary positions."

Nevertheless, six Education Department staffers have recently been busy sorting through the pile of applications. The most promising are put in a large red looseleaf binder for back-ground checks and further consideration.

So far, the winnowing process has been going slowly, prompting some grumbling from members of Congress and others who are waiting to see if their choices are picked.

Education Department officials explain that the slow going has been due in part to the lack of familiarity by Hufstedler and her top staff with the huge and sometimes competitive education community. The new secretary has been attending private sessions with many of the larger education groups to sound them out on their choices for senior Education Department staff positions.

Some education officials have complained privately, however, that Hufstedler surrounded herself with outsiders when she was appointed to head the department. The charge has led to the nickname "the Californians" for the secretary and her top staff.

So far, the only appointments to top staff jobs hve been administrative positions such as the choice of Liz Carpenter, a high-profile press officer during the administration of President Johnson, to head the new department's public information office.

"We were a little slow originally, but I think we've speeded up the process," said Richard Beattie, a New York attorney and former assistant to Health, Education and Welfare chief Joseph Califano, who was brought in last month to direct the startup process.

Beattie's first act after he took over was to reorganize the department's slow-moving recruiting program. Some applicant lists had grown to unwieldy proportions, he said, including one list of 120 names for the post of elementary and secondary education secretary.

"For some people the job-seeking process can get pretty frenetic," said Beattie. Two applicants for top jobs turned up -- resumes in hand -- on his front doorstep the week after his arrival he said.

Beattie predicted that despite its troubles the new department would have its final choices for its top jobs in hand by the end of next week.

But there have been some signs that those choices may not be eager to join up.

"Those jobs could be very short-lived," said one education expert, who was recently consulted about prospective top staffers by department officials.

The best choices already have good jobs, he said, and are closely watching the possibility that Hufstedler -- who was a highly respected member of the California Supreme Court before being chosen to head the Education Department -- may depart for the U.S. Supreme Court when an opening appears.

"Everyone knows how the game is played," said the expert, who asked not to be identified. "When the top person goes, the first thing they do is clear out the next layer too."