ANNAPOLIS -- They've been in office only four months, but the new leaders of the Maryland Democratic Party already are feuding. The party's new chairman and vice chairman are scarcely on speaking terms over how to handle the 1988 elections.

Party Chairman Rosalie Reilly and Anne Arundel County Executive O. James Lighthizer, party vice chairman, are battling over fund raising and the use of paid consultants for next year's races.

But party regulars watching from the sidelines say what's really going on is a nasty struggle for power between two otherwise genial politicians. Reilly, 57, is Montgomery County register of wills and a longtime party activist who perhaps has reached the pinnacle of her career in state politics with the party chairmanship. Lighthizer, 40, is a new-breed Maryland politician unaccustomed to second-banana status.

Lighthizer, chief fund-raiser for the party, wants to sign up Potomac Survey Research Associates, a Montgomery County consulting firm -- headed by prominent political pollster Keith Haller and part-owner Lanny Davis, a Democratic national committeeman for Maryland -- that was hired by the party in the 1986 elections to market a data base on voter information. Reilly has rejected the idea, at least for now, saying that the party can't afford to squander money on high-price consultants.

"The buck stops with me," Reilly said. "We don't need the services and we don't have any money right now." Reilly argues that Democrats are not facing the kind of challenges in next year's congressional races that warrant major spending for consultants.

But Lighthizer, who was chairman of a committee appointed by Reilly to look into the effectiveness of PSR's work in the 1986 elections, thinks the firm should continue and expand its operation for the party and its candidates.

In 1986, PSR set up and marketed Maryland Campaign Central, a program that, for a fee, provided candidates with access to a sophisticated data base of voter information. Some of the fees paid by the 102 candidates who used the system went to party coffers.

"It's a sales tool," said Lighthizer, adding that it shows donors concretely why their money is needed and how it's being spent. "It's tough to raise money for the party. This is a tangible thing that the party does," he said.

Lighthizer was asked to raise funds for the party by Gov. William Donald Schaefer, and he believes he needs to hire a staff or consultants, something he said Reilly has not allowed him to do.

"If it wasn't this issue, something else would have cropped up," said one state official close to the situation.

Lighthizer said he intends to make "every effort" to work with Reilly. "Hopefully, we'll get this thing ironed out," he said.

Does Reilly think they can work together? "God, I hope so," she said.

The consultant issue may be resolved by the party's executive committee at its meeting Monday.

Unless the two combatants can find some middle ground before then, one of them stands to get his or her feelings hurt.

So far, Schaefer, who picked Reilly and Lighthizer for their posts, has stayed out of the fray. But some of Reilly's friends were concerned that Schaefer did not invite her along when he organized a meeting on the state yacht of top Democrats to discuss Maryland's role in the 1988 presidential race.

Ultimately, it may be up to Schaefer to call off the feud.

Maryland Is a State of Mind

Six months ago, Schaefer mulled the mind-set of Montgomery County, which is in a large region he once referred to as the "foreign outland areas." Pondered Schaefer: "Where does Montgomery County really fit? Is it Washington? Is it Virginia? Is it Maryland? That's something I think I'm going to have to figure out."

Though the governor may not be ready to embrace the Maryland suburbs of Washington, he's all but colonized another border area far from his native Baltimore. During a news conference on tourism last week, Schaefer, fresh from a trip to the lower Eastern Shore, encouraged visits to the region. He found Tangier Island "just spectacular" and pronounced it "one of the hidden treasures of Maryland."

It's true -- Tangier Island can't be found on a map of Maryland, but it's not entirely undiscovered. It's part of Virginia.