Resurrecting Jimmy Carter as a simpering heavy in a Republican campaign commercial may be "kind of a small thing," as House Speaker Tip O'Neill complains. On the other hand, it may create the impression that some people are mourning Carter's political demise.

An elderly woman in the 30-second spot appears to be sobbing at the sight of Carter seated at a table by a bowl of peanuts. If you tune in a second late and don't listen closely to the "voice-over," you might think she is a heartbroken Carter partisan.

Actually, like the other stricken folk in the scene, she is supposed to be grieving over the 12.4 percent inflation rate and high gasoline prices left her by our former president who, out of respect for the office, does not speak on the show. The actor playing O'Neill, a beefy fellow straining the buttons on his three-piece suit, is limited to a gloating guffaw as the voice says, "To the Republicans in Congress, we leave the real problems."

The "Last Will," as this opus is called, has rather too much plot. It opens with a bony-faced lawyer reading Carter's lamentable bequests. Midway, the slightly defensive message is intoned: "Republicans are trying to make things better." Obviously, they have failed with the sobbing senior citizen who reappears, dabbing her eyes, while a male contemporary seeks to comfort her and the Carter look-alike grins and bobs his head, as if agreeing that he made a mess of it.

The commercial--with a companion piece called "Camper," which shows a happy foursome taking off on a fishing expedition, thanks to reduced inflation--is supposed to make things better for Republicans running for Congress this fall.

The Republican National Committee and the National Republican Congressional Committee have sunk $1.7 million into production and air time for the little gems.

But ultimately, all questions about political theater come down to one: "How will it play in Peoria?"

Unfortunately, the leading expert on the matter, House Republican Leader Robert H. Michel of Peoria, was unable to give an answer. He missed the screening last Friday. He missed the big press premiere yesterday. He has been trapped with one or another of the roving bands of budget-makers who ply Capitol Hill, trying to write documents that will not completely repudiate the present occupant of the White House while not costing them their seats.

The people of Peoria may not be terribly interested in the fact that, as the voice-over says, President Reagan has "cut the growth of government spending and brought inflation down." High interest rates are tormenting its farmers and small businessmen.

It may be that Peoria is worrying that Democrats are not getting sufficient share of the blame for their woes.

But Peoria has other things on its mind, such as an unprecedented rate of unemployment. Last week, its previously recession-proof major industry, the Caterpillar Tractor Co., laid off 8,000 workers worldwide, 4,000 of them in the local plant. The happy campers of the commercial have few counterparts in the Peoria area today.

The only thing consoling to Republicans in last week's catastrophe at "Cat" was the loyal statement of the company spokesman:

"Some people would like us to blame Reaganomics for the situation, but that would be too simplistic."

He reflected what Reagan still has going for him--the reluctance of voters to admit that they might have made a mistake in November, 1980, and their aversion to contemplating another failed presidency.

What might do more for Peoria than "Last Will" and "Campers" would be a commercial attesting to Reagan's commitment to Social Security.

Michel, on seeing that the Senate "compromise" budget proposed a $40 billion cut in Social Security funds, went into orbit last week.

"You've got to take that off the table," he cried, although he is not given to melodramatic statements likely to give aid and comfort to the Democratic enemy.

Reagan thinks he has kicked the habit of kicking Social Security. Last year's firestorm after he proposed cuts instructed him in the need to bite his tongue when discussing this most popular of big government programs.

But, at his news conference last week, having gritted his teeth and made assurances to current recipients, he was asked about those coming along and blurted out another statement guaranteed to send the apprehension index soaring. Today's toilers may pay more in taxes than they would get back in benefits. "And they would be better off if they had that money in their own hands to buy a retirement policy of some kind," he said.

Bringing back Jimmy Carter may be a nostalgia trip for the Republicans and fire them up to a replay of the 1980 campaign. But it's risky. The way things are going, people who had forgotten all about him might begin to think that he wasn't so bad after all.