PARRIS GLENDENING might well wonder whether the voters in Prince George's County elected him to run their local government or to walk the plank. If there was one thing Mr. Glendening wanted with him if he won, it was voter approval of the "TRIM Plus 4" proposal to raise the strict flat- dollar ceiling on property tax revenue. Without this modification, he repeatedly warned, the county could find itself financially crippled and without sympathy or relief from the rest of the state. Fine, said the voters, who went ahead and elected Mr. Glendening by a landslide -- while shouting down the revenue modification.

Something will have to give -- and it won't be Annapolis. After all, how many delegates and senators from other parts of the state are going to shed any appropriations tears for Prince George's until the county digs into its own shoes for more money? What will give, unless new money is raised some other way, will be the public school system and almost every other function of local government, pinched by the sheer weight of inflation alone. Even when you allow for future increases in income and other tax yields because of inflation, you're staring at a drain of perhaps $36 million a year.

That's all right -- if everyone is prepared to accept cuts of 400 to 600 public schoolteachers a year and similar blows to the budgets for all other government services. But as Mr. Glendening, coming on as Winston Churchill, noted, "I do not intend to preside over the liquidation of services in Prince George's County." Instead, he is calling on selected experts to study alternative revenue sources and to report back by inauguration day, Dec. 3.

There aren't a lot of options. Adjustments in state and federal formulas for assistance are politically and financially unlikely.

One approach -- and it couldn't be just for Prince George's, since it would need the legislature's approval and acceptance by business interests -- is authority from Annapolis for an optional penny local sales tax in the state's larger localities. Recent growth and inflation patterns indicate that such an increase could yield perhaps $32 million a year for Prince George's -- which would almost match that $36 million that the county stands to lose automatically thanks to TRIM.

Whatever course the county chooses, it should do so quickly. The legislative doors in Annapolis open in two months.