The fragile coalition pieced together by Maryland State Sen. Melvin A. Steinberg (D-Baltimore County) in his attempt to unseat Senate President James Clark Jr. (D-Howard) is tottering.

Steinberg had lunch yesterday with seven of the nine members of the Baltimore City delegation and was told that he has no more than three firm votes in the delegation. A week ago he thought he had six, possibly seven, sources said.

The waffling by the city senators appears to stem from concerns that the deal Steinberg had offered the city -- to replace Sen. Laurence Levitan (D-Montgomery) as chairman of the budget and tax committee in favor of Baltimore Sen. Clarence W. Blount -- would create a war between the city and Montgomery delegations.

Steinberg was told by the senators that the city did not want to create a war with Montgomery and would not mind if Levitan retained the chairmanship. The senators told Steinberg that, if forced to choose between an alliance with Montgomery or an alliance with Baltimore County, they are inclined to go with Montgomery. "They're our most natural ally," said one. "We're going to sit tight at least for awhile and see what happens."

The key man in the city delegation is Blount, who yesterday told Steinberg that if the vote were held now he would be with Clark. That means Steinberg or Clark would probably have to deal with the city and Montgomery as a bloc and their votes appear up for grabs.