Leaders of Prince George's County's largest public employe union last night called a strike for today that they say could virtually shut down the county government.

The strike, the product of a bitter dispute between County Executive Lawrence J. Hogan and officials of the American Federation of State, County and Municipal Employees, climaxes a 19-month contract dispute.

Hogan's aides predicted yesterday that any strike would fizzle and said they have contingency plans to operate the government without the strikers. They did not elaborate on these plans.

After months of court fights, strike threats and verbal blasts from all sides, the 1,500 members of the union's five county locals plan to mount 11 picket lines around county facilities this morning.

A glimmer of hope remained that the strike will be cut short. Union officials said they have agreed to meet this afternoon with county negotiators and a federal mediator.

Although county police, represented by a different union, will remain on the job, the AFSCME plans to deprive the county of its jail guards, road crews, landfill operators, building inspectors, senior-citizen workers and secretaries.

Union officials say buildings will go uninspected, garbage trucks will have no place to dump their refuse, emergency telephone operators will not be on hand to answer calls, paperwork will pile up and the jail may go untended. Hogan has said he will fire any guards who strike.

The county has never before had a full-scale strike of its public workers, although other unions have staged work slowdowns.

Various union officials -- picket captains, shop stewards, representatives of the international union and the locals' presidents -- worked into the night stapling together picket signs and preparing strategy. They claimed that Hogan had forced the strike.

"We've been treated with contempt since the day he walked into his office," said Ernie Crofoot, AFSCME's state representative. "He's backed the employes into a corner and then said they don't have the guts to go out."

At issue is neither wages nor benefits -- points that were resolved months ago -- but more philosophical concerns. Hogan has said he will not agree to provisions that would grant the union a full-time chief shop steward, provide 126 paid leave days for union leaders to attend conferences and guarantee the union a closed shop.

Union officials say that Hogan, a Republican, is out to destroy public employe unions and is going after them for political reasons.

The current confrontation is the product of conflicting personalities and county tradition, which holds that colorful and strident rhetoric is a requirement of political success. On one side of the battle line is Hogan, who has made his political name in this conservative blue-collar county as a gut-punching political fighter. On the other is the union's business representative, Paul Manner, an ex-Marine who does nothing to mask his dislike, personal and political, for the county executive.

Acutely aware of his reputation and the political success that it has brought, Hogan is determined to show that unlike county Democrats, he is tough on unions, even when the courts have told him that his activities have been improper and unfairly political.

The bad blood between Hogan and Manner began during the 1978 elections, when Manner and AFSCME aided Hogan's Democratic opponent. The mutual dislike has only increased with time.

As Hogan's labor woes have mounted, with the AFSCME contract the principal source of conflict, Manner has accused Hogan of being a "political opportunist" willing to "beat up on public employes" simply to increase his popularity in political opinion polls.

Hogan has responded that the current contract dispute is the product of intransigence on Manner's part and a disire by the union to help the political fortunes of county Democrats.

Hogan's belief that the unions and the Democrats are conspiring to do him political damage led him at one point during the current contract conflict to veto a tenative agreement with the union that his own negotiators had worked out. He told aides that he would not approve the agreement because Manner and the all-Democratic council had tried to use the contract dispute to help Hogan's political adversaries.

The union and the county first sat down to work out a new two-year contract in February 1979. Four months later, when AFSCME's contract expired, the union and the county were still unable to agree on several key provisions, including cost-of-living increases.

Those issues were worked out during the next few months and on Feb. 13, 1980, Hogan's own negotiators union officials initiated a tentative agreement that was felt to be quite favorable to the county.

It granted the union members a 4.7 percent cost-of-living increase for the fiscal year ending July 1, 1980, and 5 percent for the following year. The county's non-unionized employes had received such increases from the county's executive branch months before.

When the tentative agreement was presented to Hogan for final approval, however, he refused to sign it, according to county officials familiar with the incident. Hogan told his aides that it would make his political adversaries look good and, according to one account, said, "A strike is sometimes good politics."

When the incident became public the next day, Hogan said he vetoed the agreement because of "unacceptable" provisions in it relating to minor health and economic benefits. By the next week, however, he had changed his objections.

The health and economic benefits issue was resolved, but Hogan objected to provisions that had been in AFSCME's contracts for the last seven years that gave members of the union paid leave days for union leaders and provided a closed shop. He also objected to a new provision that would have granted the union a fulltime chief steward.

The union immediately charged Hogan with violating the county's labor code for turning down the tentative agreement. After extensive hearings, an independent hearing examiner supported the union's contention, chastised Hogan for allowing politics to enter labor negotiations and ordered Hogan to implement the agreement immediately.

A Circuit Court judge just a few weeks ago upheld that finding, and Hogan promptly announced he would appeal. The union responded by saying it would strike.

After months of expensive legal maneuvers and hours of closed -- door meetings between the two sides, three issues separate the union and the county: paid leave for union leaders to attend meetings, a full-time chief steward and a closed union shop.