Prince George's County Executive Parris Glendening and Baltimore City Mayor William Donald Schaefer announced a joint tax plan yesterday which, if enacted by the General Assembly, would raise $84.5 million next year for their financially troubled jurisdictions.

Their proposal, which included a measure to raise the state income tax by 1 percent, immediately drew a mixed response from legislators. Several Prince George's legislators said they doubted it would pass and that they were angry that Glendening had not told them ahead of time about his conference with Schaefer.

Glendening later said he had, in fact, informed the delegation. The difference in opinion and the legislators' anger was one more sign of the growing split between Glendening, newly elected in November, and the delegates.

The Glendening-Schaefer proposal, which would raise new revenues to be spread around the state, would cost taxpayers about $289 million during the fiscal year beginning next July 1. First, the tax rate would be increased from 5 percent to 6 percent on incomes of more than $15,000. That would raise $141.7 million, Schaefer said. A second proposal would allow the counties to increase their surcharge on the income tax, the so-called "piggyback tax," from 50 percent to 60 percent of the amount charged by the state, which could raise another $147.6 million.

Schaefer and Glendening proposed that the state use all but $26 million of the additional money to increase funding for two educational programs that assist poorer jurisdictions.

"We can't wait for next year," said Schaefer. "If you're standing on a soup kitchen line, if you're standing in a line and they're asking you to pay your mortgage, I don't think they're very interested in words like 'wait until next year.' " Schaefer strongly criticized Gov. Harry Hughes and some members of his own delegation for what he called their unwillingness to recognize his city's financial problems.

In similar but less dramatic language, Glendening said the county faces a shortfall of $35 million in its fiscal 1984 budget, he said, and the possibility of up to 1,000 layoffs. Although earlier Glendening estimated the layoffs at approximately 600, he said that the figure was revised upward to include the positions that must be eliminated to pay costs of unemployment compensation and building a new, court-ordered jail.

Glendening said he had explained the package to some Prince George's delegates and County Council members Tuesday night at a meeting in the Annapolis apartment of Del. Charles (Buzz) Ryan, chairman of the county's delegates. A state senate representative had been invited but did not come, he said.

Ryan disputed Glendening's version, however, saying Glendening "mentioned" the joint press conference but provided no details about what would be said there.