Chances dimmed today that the General Assembly will permit Prince George's County to increase its local income tax, a key ingredient in County Executive Parris Glendening's plan to offset a projected $35 million budget deficit.

The blow came when Speaker Benjamin L. Cardin and other leaders of the House of Delegates came out against legislation that would allow the county to increase from 50 percent to 60 percent the add-on or piggyback amount it tacks on to the state income tax. The proposed increase would generate about $20 million in additional revenue.

"The bill isn't dead, but they've certainly scheduled the funeral," said Del. Charles J. Ryan, chairman of the county's delegation. "With Ben against it, we've got troubles."

Glendening conceded today that the proposal is in jeopardy, but said he isn't giving up on the idea. He and Ryan are scheduled to plead their case to Cardin next Tuesday.

"It's certainly going to be difficult, but a month ago people were predicting we'd never get it out of the delegation and we did," Glendening said. "We have nothing else left in the hat other than firings and service cuts. We'll make our case to him [Cardin] as clearly as we can and hope he understands."

The county delegation gave its blessing last Friday to the increased piggyback tax and to a second Glendening proposal that would raise the county's business property tax. The latter, which would produce about $10 million a year, is expected to pass with little difficulty.

The county has had trouble generating sympathy here for its budget gap because its voters have twice supported an amendment to the county charter that limits to about $142 million the amount the county can collect annually in property taxes.

Cardin and the House leadership took the position this morning that to give the county the extra taxing authority would set a precedent that might encourage other counties to make similar requests in the future. They also said the timing is bad because it comes when a statewide tax increase is likely.

Del. Gerard F. Devlin (D-Prince George's), vice chairman of the Ways and Means Committee, said that during the leadership meeting Cardin said "he was against it [the piggyback tax], planned to oppose it and thought it would certainly die in committee. I said, 'Ben, don't sugarcoat your answer; tell us what you really think.' "

After the meeting, Del. Dennis C. McCoy, a member of Ways and Means and chairman of the Baltimore delegation, told Devlin that the city also would oppose the piggyback tax. Glendening learned of his new problems when Del. Frederick C. Rummage, another Prince George's member of the leadership, called him with the news.

"I had already told him after he got it through the delegation that he was overestimating the importance of that vote," Rummage said. "That was just one step. There are still six left. And I guess the next one will be very tough."

Devlin said he did not know how many votes Prince George's might have in the 23-member Ways and Means Committee if a vote were held today. Glendening said he planned to spend a lot of time here lobbying the committee.

"There seems to still be a perception out there that we're asking the state to bail us out," he said. "We aren't. We're just asking for the chance to bail ourselves out this one time. We aren't even asking for a permanent increase."