One of George Sheldon's campaign leaflets depicts him warmly embracing an elderly woman. His arm is draped protectively over her shoulder, and she appears comforted.

Viewed another way, Sheldon, 35, is holding on for dear life.

The state legislator is staking his underdog bid for Congress on elderly voters. He is running in Florida's new 9th Congressional District, a three-county region north of Tampa Bay on the west-central coast where an estimated 60 percent of those likely to vote Tuesday are 55 or older.

That is why Sheldon casts his race against Republican Michael Bilirakis as "a referendum on the Republican cuts in Medicare and Social Security."

In one television ad, Sheldon sits with senior citizens on a porch and promises to "honor thy father and thy mother." His newspaper-style brochure features a clip-out "resolution to protect social security" with spaces for voters to sign.

He recently held a "rally to protect Medicare and Social Security" with Rep. Claude Pepper (D-Fla.), the Miami octogenarian who has become the country's biggest Democratic drawing card this year.

Bilirakis, 52, a conservative in his first race for public office, responded that Sheldon is using "un-Christian" scare tactics to snare elderly votes.

He sought to divert attention from Pepper's visit by calling a news conference with GOP National Chairman Richard Richards, who complained that "every week some Democrat demagogue is down here telling. . . the elderly that they are in danger of losing their Social Security."

Bilirakis said he, too, would vote to protect Social Security, though he noted that some of the system's expenses can be trimmed through elimination of "fraud."

Though clearly on the defensive concerning Social Security, Bilirakis is nevertheless the favorite. A millionaire lawyer and businessman, he scored a startling upset in the GOP primary.

Bilirakis campaigned energetically, and his pledge to be a "true representative of the people" struck a nerve with Republican voters. They apparently weren't troubled by his comments on issues that were so vague that one local political columnist wrote: "He just hasn't done his homework."

Though the largely rural district has35,000 more Democrats than Republicans, Democrats don't turn out as well as Republicans. Sheldon has been considered one of the legislature's leading liberals of recent years, but he eschews that label in his congressional race.

"Progressive I like better," he said.

Sheldon's task is to keep Democrats in the fold and attract Republican crossovers. To that end, he plans targeted mailings to elderly voters of both parties, as well as television commercials featuring Pepper.

Like Democrats across the country, Sheldon has attacked Republican economic policies with increasing vigor since the recent announcement that national unemployment had topped 10 percent. Both candidates expect to spend about $300,000.

The emphasis on elderly voters is everywhere in Sheldon's campaign. His fund-raising committee is entitled "Senior Citizens and Working Families for George Sheldon." Volunteers from the National Council of Senior Citizens and the National Association of Retired Federal Employes are manning his offices in Pasco and Pinellas counties.

Bilirakis promises to maintain an advisory "task force" of senior citizens if elected. And he has tried to exploit Sheldon's legislative record, particularly on crime. Without citing specifics, Bilirakis' campaign manager Donna Frangakis said that Sheldon has been "very soft" on crime in his eight years in the legislature.

Sheldon may have partially blunted attacks on the crime issue, however, by sponsoring a state constitutional amendment on the general election ballot. The amendment would permit judges to deny bail to certain defendants accused of serious crimes.