Plans for a $6 million performing arts center in Arlington's Pentagon City died yesterday after County Board members expressed skepticism about whether county residents would support the facility or be willing to pay additional taxes to underwrite its operations.

The proposal, endorsed by numerous arts groups, won the backing of only board member Ellen M. Bozman. Board Vice Chairman Mary Margaret Whipple said she "reluctantly and sadly" would not second Bozman's motion, thus allowing to the board's three other members to avoid having to cast votes on the center.

Whipple and Bozman had been the staunchest supporters of the center, a 1,200-seat, professional theater that would have housed the community productions now performed in schools. It would have been part of a large shopping mall planned for Pentagon City.

"This is a unique opportunity for Arlington to improve by a giant leap the quality and vitality of the county," said Faye Lyle of the Arlington Metropolitan Chorus, one of several supporters who outnumbered opponents 2 to 1 during the board's four hours of deliberations.

Whipple and Bozman said the county should take advantage of an offer from Melvin Simon & Associates, the mall's developers, to incorporate the center in its plans because studies showed costs would double if it were built elsewhere.

They contended that a projected $325,000 annual deficit for the center could be offset by private gifts and fund-raising events, and they pointed to the $7.5 million in county revenue that the mall is expected to yield annually.

But their arguments failed to persuade Board Chairman John G. Milliken and board members Michael E. Brunner and Albert C. Eisenberg, who said that they supported improved facilities for local performers but suspected that the projected costs and deficits might be low.

Eisenberg said the center "falls between 'nice-to-have' and 'have-to-have,' " especially with anticipated cuts in federal aid that may require the county to boost support of other programs.

Brunner, the only Republican on the five-member board, cited similar concern over priorities and noted that such large projects usually are placed before voters in bond referendums. He said the apparent lack of strong community support for the project could result in a "fiasco."