Dorothy Height and her National Council of Negro Women are on a laudable crusade -- but one that is about as difficult as a mission to Mars.

They are trying to revive the concept -- and admiration -- of the extended black family, whose bonds and pressures once were a powerful barrier against dropping out of school, engaging in crime, getting pregnant out of wedlock and using ''reefers'' and other illegal drugs.

Height and her colleagues have staged huge rallies in Los Angeles and Detroit and will bring their campaign to the nation's capital on Sept. 12. They will find here, as in every other city, that the forces buffeting black teen-agers and black families are so beyond the influence of the National Council of Negro Women or any other black group that even optimists are inclined to weep.

In a brilliant commencement speech at Howard University in 1965, President Lyndon B. Johnson talked about how slavery and the fallout from it had left black Americans in a gateless cycle of poverty, ignorance and despair. Height and her colleagues are trying anew, and wisely, to find some gates out of that vicious circle.

Their first challenge is to figure out where to start, what social, political and economic priorities black Americans should make.

I recently had six hours of interviews with Supreme Court Justice Thurgood Marshall for a special on the U.S. Constitution that will air here on Sept. 13, the day the women end their Washington crusade. I asked Marshall which of the 29 cases he won as a civil rights lawyer before joining the judiciary (he lost only three) he regarded as most important. He chose the 1944 decision knocking out the ''white primary'' in Texas and the 1954 decision outlawing public school segregation.

''The voting one, of course, is the most important one,'' Marshall said. ''Although much can be done in the educational field, education alone won't do it. We had education before we had voting, and it didn't work. You don't make it without the vote.''

Those seeking to restore the health of the black family may argue that blacks never have had access to equal education, and thus they have no chance at jobs that deliver the incomes essential to social and economic justice. Some will argue, plausibly, that the absence of education makes it impossible for millions of youngsters to say no to drugs, to escape the lures to self-destructive promiscuity.

But there is a Catch-22 here that black Americans cannot seem to escape. Recent history makes it clear they cannot gain equality of educational opportunity, or parity in the job market, if they do not impose relentless, even ruthless, political pressures. Yet, blacks cannot wield political power effectively where lack of education produces apathy, or where rage feeds the cliche' that ''all honkies are alike'' or where pride says ''vote for the black candidate, even though you know he or she cannot win.''

The National Council of Negro Women has chosen to face up to some wrenching dilemmas, some problems that call for very controversial decisions, some areas of social malaise where no solutions may ever be possible in this society.

But Height and her colleagues are trying. If a lot more groups make brave efforts, at least we can believe that black children, teen-agers and families are not going to founder in a miasma of hopelessness.