Can labor keep its big promise to Mondale?

Unions are looking to the Super Tuesday presidential primaries as a first major test of their ability to turn out votes for Walter Mondale and reverse setbacks in New England.

The credibility of the AFL-CIO's pledge of support for the former vice-president is at stake.

The federation of 96 unions with 13.5 million members gave Mr. Mondale its unanimous early endorsement for the Democratic nomination. With the endorsement went commitments of millions of dollars in financial backing and hundreds of political workers.

So far, the muscle provided by unions in support of Mondale has proved to be flabby. Although labor's favorite candidate won in Iowa, CBS and other polls indicated that unions failed to turn out an expected strong Mondale vote and that many teachers and blue-collar workers ignored the AFL-CIO and their unions to cast ballots for his opponents.

Similar exit polls indicated that unions failed to muster strong Mondale backing in New Hampshire, Maine, and Vermont as well. Labor did not turn out large numbers of union members, and an unexpectedly high number of union members chose Gary Hart.

The AFL-CIO plays down the importance of the early reversals, describing the New England states as normally Republican and not strongly unionized. But disappointment is hardly concealed; labor worked hard for votes it did not muster.

In Maine, polls indicated that Hart received almost as many ''labor household'' votes as Mondale in the state and that many others who voted for Hart did so in protest of Mondale's ties to organized labor and other special-interest groups.

In Iowa, Mondale had the backing of strongly organized teachers and other union members. Exit polls indicated that while 62 percent of those in union households voted for Mondale, teachers gave him only 38 percent of their ballots. Even so, labor was considered a key factor in Mondale's Iowa victory.

The AFL-CIO's Committee on Political Education (COPE) considers the Iowa campaign more of an indication of what will happen on Super Tuesday, March 13, and in later primaries.

Larger concentrations of blue-collar unionists will be involved in Massachusetts, Rhode Island, Alabama, Georgia, and Florida - states offering winners 432 delegates as the prizes - and in Washington, Oklahoma, Hawaii, and Nevada, where another 173 delegates are at stake.

Mondale had formidable early leads in the Southern states, but his success could depend on how many black unionists vote for Jesse Jackson and how many in the swelling ranks of young union members are attracted to Hart's ''new leadership'' call to arms.

A significant number of Southern union members are now blacks, and young unionists are showing a growing impatience with older ''establishment'' leaders of their unions.

Unless Mondale scores major victories in Tuesday's contests, enough to take away the momentum Hart has developed, labor political strategists are afraid that what was originally considered an easy nomination bid for Mondale could turn out to be a hard battle, resulting in a weakened Democratic position in its fight for the White House in November.

COPE and union political workers still predict that the Midwest and the big industrial states - New York, New Jersey, Pennsylvania - will make Mondale the party's nominee. Their confidence, however, now appears a bit shaky.

Mondale recently warned a regional AFL-CIO political conference in Boston that he could lose his presidential bid if labor does not give him strong and active support, something he said has not always happened.

''You always endorse me, but you haven't always worked very hard, and there is a difference,'' Mondale said in words that could be prophetic. ''We are going to win if you're with us actively and not just in words. We'll lose if you are not with us.''