Across the country in this midterm election, Republicans enjoy the advantages of lavish finances and high-tuned, computerized campaign organizations.

But here in Maine, these assets appear to have been squandered to the point that a once heavily favored Republican is struggling in the race.

Having run through $650,000 on computer campaign assistance, television spots and direct mailings that have mostly blown up in his face, Republican Rep. David F. Emery has watched his lead over appointed Democratic Sen. George J. Mitchell shrink from a reputed 36 points to minus 8 in opinion polls. He has plunged $100,000 into debt without opening a campaign office in any of Maine's three major cities or printing a single campaign brochure.

A year ago, the Maine Senate seat looked ripe for the picking by the Republicans. Mitchell 49, appointed to the vacancy created in 1980 by Edmund S. Muskie's resignation to become secretary of state, was bucking "the curse of the appointed senator," which has seen most of them fail to win election in their own right.

Mitchell looked especially vulnerable. A veteran Democratic worker, he had lost his only bid for elective office -- a race for governor in 1974 -- and had been out of sight as a federal judge for several years before his appointment. There was even a threat of a serious primary challenge from ex-governor Kenneth B. Curtis (D).

Meanwhile, the Republicans had managed to avert a primary fight between their two representatives, and had settled on Emery, 33, the senior of the pair, who claimed to have a poll putting him 36 points ahead of Mitchell. While no one thought that margin would hold as Mitchell became better known, the odds looked good.

Emery, a personable, folksy electronic engineer, combined handshaking with sophisticated computer mailings to become one of four Republican challengers in the country to defeat an incumbent Democratic House member in the Watergate year of 1974. In each subsequent election, he added to his margin in the blue-collar district, winning with 68 percent in 1980.

But two weeks ago Emery was forced to change campaign managers. He cleaned out his staff and gambled that the new folks could undo in two months the self-inflicted damage of the previous 12.

Thomas Daffron, who managed Sen. William S. Cohen's (R-Maine) 1978 campaign and more recently was Cohen's administrative assistant, has come aboard at what is rumored to be the highest salary ever paid a Maine political manager. Sitting in a borrowed office here the other day, Daffron looked at the situation he inherited:

"We have to raise money and hire good staff, and neither one is easy to do in August. Mitchell has run a good campaign. They have a new TV buy starting Sept. 7. We have nothing. We have to try to survive in September. If we can stay competitive, then maybe we can get the campaign back on the issues, and we have a shot. But if the trend can't be stopped, we could be blown away."

The saga of Emery's self-inflicted wounds is almost unbelievable:

The congressman was criticized in the press for "negative campaigning," when he used his May speech to the GOP convention to label Mitchell "schizophrenic" and a "chameleon."

A telvision spot in which Emery claimed that his engineering background had given him the answer to the acid rain problem enabled Mitchell to respond that Emery had neither sponsored nor testified on acid-rain legislation, as Mitchell had done.

A mailing to veterans claimed that Emery had a 92 percent favorable rating with the Veterans of Foreign Wars and that Mitchell's rating was zero. The organization immediately said its rating was made a month after Mitchell's appointment in 1980, and showed clearly that it was too soon for him to be evaluated. Editorials decried Emery's "campaign of distortion," but it may have been just ineptitutde. The same mailing spelled the name of the senior senator from Massachusetts "Kenedy."

Another mailing, to senior citizens, said Emery was rated higher than Mitchell by the National Alliance of Senior Citizens. The Mitchell campaign held a news conference to point out that the alliance was a small group, linked to the National Conservative Political Action Committee, and said Mitchell rated higher than Emery with the larger National Council of Senior Citizens. Once again, Emery was scored in editorials. "Those stories dominated the summer news," Daffron said, "and the campaign did nothing to create other news." But the fact that this was a summer phenomenon keeps the Mitchell camp from being overconfident. "If this were October, I'd feel better," said Larry Benoit, Mitchell's manager. "In summer, people tune politics out."

Emery's slips aside, Mitchell has worked hard to strengthen his position. Since his appointment by Gov. Joseph E. Brennan (D), he has been back in Maine every weekend the Senate was not in session. While he is considered no match for Emery at handshaking, he has shed some of the stiffness of the courtroom and developed a humorous touch.

Luck has been with him. The Curtis primary challenge threat disappeared after the ex-governor had a mild heart attack. Mitchell has been aggressive on the issues, hopping early on the Social Security question with a state-wide television talk aimed at the large number of elderly voters.

He has taken full-page newspaper ads to blast Emery's "distortion." He sent out his own mailing to veterans last month, including a bread-and-butter letter he received last May from Chief of Naval Operations Thomas B. Hayward, thanking him for his "unswerving support" of the Navy. Daffron calls that a "dubious" use of the Navy letter.

Economics is the issue both sides expect to dominate the final weeks of the campaign, if Emery gets back on track. As deputy House whip, Emery has been a down-the-line backer of Reaganomics. Mitchell supported many unsuccessful Democratic amendments to the 1981 tax bill and budget, but voted for both in the end. This year, he opposed both the budget and tax bills.

Emery says that record shows Mitchell is doing a political "flip-flop" to cloud the fact that he is basically a "tax-and-spend liberal." Mitchell says he has shown "independence of judgment," while Emery has "voted in lock-step with the administration, even when its program conflicted with the interests of the people of Maine."

The issue cuts both ways, according to the rival camps. Reagan is personally popular here, but polls show almost as many doubters as believers in his program. The economy is mixed, with growth in the Portland area and southern Maine, hard times in the north woods.

A second issue emerged last month when Emery became the only House member of either party in New England to vote against the "nuclear freeze" resolution. Mitchell has advocated such a freeze for more than a year. Maine papers contrasted Emery's position with that of Rep. Olympia J. Snowe (R-Maine), the other House member.

That was but the latest example of the tension between them. Snowe, as charismatic and polished as Emery is down-home and direct, was considered by many, including Mitchell, as a tougher potential opponent.

Though she bowed to pressure in 1981 to let Emery run, she has not hesitated to publicize her differences with him, and only last month agreed to join Cohen as "co-chairman" of the Emery campaign.

The highly popular Cohen also had kept hands off the Emery campaign until now. Despite Daffron's involvement, there is uncertainty over how far Cohen will move. He said the other day he would make "appearances from time to time and perhaps a commercial, but basically you cannot transfer popularity in this state. My endorsement won't change 10 votes.

Behind all the specific issues is the question of what kind of senator Maine wants. Emery has been more of a figure in his district than he has in Washington. But Maine has a tradition of significant senators, from Margaret Chase Smith to Muskie to Cohen. Mitchell is trying to link himself to that tradition with the slogan, "George Michell. A Senator for Maine -- and the Nation."

But he has not forgotten how he got where he is. At a Democratic picnic in Cumberland last Sunday, he said, "I want to pay tribute to two men -- Gov. Joe Brennan, without whose good judgment I would not be in the Senate, and Dave Emery, without whose bad judgment I might not get to stay there."