The Democrats are setting out to do for Dixie the Elephant what the Republicans in 1980 did for Tip O'Neill.

A 30-second television spot that began airing yesterday in selected markets depicts Dixie, an amply girthed symbol of Republicanism, blundering her way through a china shop, smashing crockery labeled "Social Security" and trampling other precious bits of America's liberal legacy.

A view of Dixie's stern, waddling down the aisle and knocking over the shelves, fills the screen, while the announcer says, "Two years ago, we trusted the Republicans to mind the store in Washington. They promised us they'd bring prosperity and respect America's heritage of fairness and compassion. . . . The Republicans have made a mess of things."

The ad is part of the first Democratic Party TV campaign, an effort to adopt the technique the Republicans used in 1980, when an actor depicting a broad-beamed Speaker of the House Thomas P. (Tip) O'Neill Jr. (D-Mass.), driving a car that runs out of gas, was used as a symbol of Democratic incompetence.

Conceived by Democratic National Committee communications director Robert Neuman, and executed with two days of rehearsal and one of filming by First Tuesday, a Phoenix ad firm, the commercial cost $34,000 -- "$1,000 a day for Dixie and her trainer," said Neuman, "and a helluva lot for breakage."

Party chairman Charles T. Manatt said close to $1 million has been raised for the campaign, with about half of it contributed by labor unions. Because the ads are designed to support party slates or gubernatorial candidates, unions are allowed to use "soft money" -- membership dues, not voluntary political contributions -- to underwrite the effort.

An additional half-million dollars was raised from individual contributors to expand the initial purchase of air time.

Nonetheless, Manatt said, the national party was buying time mainly in secondary markets -- in Sacramento rather than Los Angeles, and Flint rather than Detroit -- in order to gain the widest exposure.

He said copies of the ads were being made available to state Democratic parties in hopes they would finance additional showings. The Republicans' 1982 ad campaign, already on the air, is budgeted at $10 million.

Dixie's destructive ramble through the china shop is one of five commercials previewed at DNC headquarters yesterday. Others, made by David Sawyer, attack the Republicans' record on unemployment, tax cuts and Social Security, using the tag line, "It isn't fair. . . . It's Republican."