When Ronald Reagan's high command heard that presidential aide Gary L. Bauer not only had invited tough-love principal Joe Clark of Paterson, N.J., to the White House but had offered him a job, the president's men were not happy.

Was it a good idea, they wondered, to link Reagan with the black schoolman who brought order out of chaos at Eastside High with baseball bat and bullhorn? They need not have worried. Clark won't be joining the White House Mess. On his Jan. 15 visit, he was hustled out of the building for a restaurant lunch without ever being near the president.

Fear of Joe Clark connotes more than reluctance by buttoned-down Republicans to embrace a rough-hewn, jive-talking black man. It typifies the Reagan administration's failure to broaden the party's base. The earnest, well-meaning moderates who now run the White House staff have no strategy for either attracting ethnic whites or breaking the Democratic hammerlock on blacks.

Clark is a potential lever for both. Thousands of favorable telephone calls from whites and blacks alike are generated by his television appearances. The antitheses of the white establishment members of the Paterson School Board who want to fire Clark are black parents who see in him some hope for saving their children. When it comes to Clark, these parents agree with conservative Secretary of Education William J. Bennett and not the educational establishment.

Alone among White House aides, Bauer understands the political potential of the Clark phenomenon. He knows the conciliatory tone of moderate Republicans never will transform the civil rights apparatus from a virtual appendage of the Democratic Party. The only hope is attracting middle-class blacks who welcome Joe Clark's harsh discipline and share the outrage of their ministers over birth control clinics in public schools.

Bauer telephoned Clark Jan. 8 to express support and offer him a job on his own staff should he be forced out or decide to leave. Not surprisingly, the flamboyant principal went public with the offer (though actually, he and Bauer agreed he should stay in Paterson).

Clark's was not a popular disclosure among White House senior staffers. One presidential aide grumbled that Bauer had offered the job strictly on his own. The unease was heightened when Clark went on national television to declare the president was behind him and then added, with exuberant hyperbole, that meant the armed forces of the United States also were supporting him.

But news that Clark was going to visit the White House generated excitement at Eastside High among blacks who supposedly loathe Ronald Reagan. A janitor asked the principal whether that meant he actually would get to see the president.

He didn't get close. Clark was hurried in and out of the White House basement, across Lafayette Square over to the Hay-Adams Hotel for lunch with Bauer without Reagan's having laid eyes on him. In fact, while newspaper accounts always talk about the president praising the hard-nosed principal, there is no record he has said a word about Clark since a telephone call in September 1983, congratulating him on ''good work in cleaning up the schools.''

The president's failure to embrace Clark publicly and his staff's concern about doing so mean they were just acting like Republicans. While fearful of offending the black establishment, the White House staff blows obvious chances to win over black voters. Suggestions that an existing vacancy on the Federal Reserve Board be filled by a black conservative encounter blank stares from the president's men.

Vice President George Bush, front-runner for the Republican nomination, talks about himself as the future ''education president.'' But at the Dartmouth debate, only Rep. Jack Kemp mentioned Joe Clark as a Republican answer to the inner-city school. If fear of him is interpreted as apprehension in Republican country clubs about a black man with baseball bat and bullhorn, the Democratic monopoly on the black vote is only reinforced.