The Prince George's County legislative delegation, which a month ago greeted with skepticism and hostility a tax package from County Executive Parris N. Glendening, voted overwhelmingly today to support that package after a massive lobbying effort by unions representing county employes.

Today's endorsement by the 23-member House delegation followed more than a week of lobbying--telephone calls, office visits, letters--by unions representing police, teachers, firefighters and other county workers who could lose jobs if the county does not fill what Glendening said is a $35 million gap in next year's budget.

The bills, which would generate about $30 million in revenues, would allow the county to increase its business property tax and the county's portion of the state income tax from 50 percent to 55 percent. They were approved by votes of 18 to 3 and 18 to 4 respectively.

After the votes, Glendening, who spent weeks trying to overcome delegation anger at his handling of the tax package, said, "We still have a long way to go." He spent several minutes after today's meeting shaking hands and thanking the delegates for what he termed "a responsible vote."

The bills now go to the House Ways and Means Committee, where their prospects are uncertain. Some legislators from other counties said they don't see why the state should pass tax measures to help Prince George's after its voters twice supported a cap on county tax collections.

Since 1979, the county has been limited to collecting about $142 million annually in property taxes because of a voter approved measure called TRIM (Tax Reform in Maryland).

In an effort to overcome legislative coolness to his proposals, Glendening and delegation leaders will spend next week lobbying the Ways and Means members and House Speaker Banjamin L. Cardin, who has been unethusiastic about the tax package.

"The effort will be to neutralize Cardin," said one Prince Georgian.

Glendening's proposals appeared to have little chance of passage at the legislature when he unveiled them about a month ago.

Primary opposition came from his own county legislators, who were upset that he had not consulted them before making the proposals public.

However, the new county executive made several peace missions to Annapolis, providing statistics on the county's budget problems, showing up at hearings and giving breakfasts at which he assured the senators and delegates that he wants to work with them. The executive received substantial help from the unions. "We did everything we could to supply them with information on the the deficits that would exist," said Mahlron Curran, president of the Fraternal Order of Police.

"I described the situation as it exists in the schools," said John Sisson, president of Prince George's County Education Association, who patrolled the halls outside the county delegation's offices all week.

Sisson said he reminded delegates that county classrooms are overcrowded and that programs to deal with gifted and delinquent children have been reduced sharply.

Despite today's success, opposition remains within the delegation. Del. David Bird, coauthor of TRIM, voted against increasing the local income tax, which would raise $22 million. "If he Glendening holds down spending and makes reasonable cuts, he can make his budget work."