Organized labor's big-stakes campaign to organize the historically non-union South suffered a major setback this week at a huge Virginia shipyard where, little more than a year ago, its prospects for a breakthrough appeared brightest.

Last winter, when the United Steelworkers of America won a hotly contested representation election at the Newport News Shipbuilding and Drydock Co., USWA President Lloyd McBride hailed the victory as a "significant advance for the cause of trade unionism in the South."

Early this year, in what now appears to be a major tactical error, the big AFL-CIO union, frustrated in its efforts to win recognition and a contract from the company, called the yard's 15,000 production and maintenance workers out on strike.

Despite a gradual return by up to 75 percent of the work force, the union was insisting up until this week that the walkout was suceeding. Then, suddenly on Monday night, the USWA "suspended" the strike in the face of legal entanglements that could prolong the work stoppage by a year or more.

While USWA officials describe the suspension as merely a "change of strategies" and say the strike may well be resumed, a number of union observers - and some officials of other unions - say it constitutes a heavy blow both to the USWA and to unions as a whole in the South.

The stakes against the Steelworkers were high from the start: a conservative political climate that breeds hostility to unions, a state government that has elevated its "right-to-work" law to an article of faith and is willing to use its police power to enforce it, a company (a subsidiary of the Houston-based Tenneco conglomerate) that has the will and wealth to withstand even the largest of national unions, and labor laws that can be skillfully manipulated to a company's advantage in postponing its day of reckoning with a union.

"There are solid reasons why the South hasn't been organized," said one labor expert, "and most of them can be found at Newport News." An- other suggested that the confluence of Virginia and Tenneco, "a marriage made in NAM (National Association of Manufacturers) heaven," was an obstacle too formidable to overcome.

"Even Alabama and Mississippi are light years away from Virginia," conceded a USWA official. "Anyone who thought Newport News would be easy was crazy as hell."

Easy or not, both the USWA and the rest of the labor movement pounched eagerly on the organizing breakthrough 15 months ago in large part because it presented a glimmer of hope on otherwise barren landscape. Unions, losing ground as jobs disappeared from their historical strongholds in the industrial Northeast and Midwest, had staked out the fastgrowing and relatively unorganized Sunbelt as their new frontier. But it was tough going. The symbol of their Dixie drive was a bitter campaign, of guerilla warfare between the J.P. Stevens Co. and the Amalgamated Clothing and Textile Workers Union, which held out little hope for a speedy resolution.

Even the powerful United Auto Workers had to go to the mat last year with General Motors over the corporation's alleged "Southern strategy" to keep the UAW out of its new Sunbelt plants. The UAW won, but not without a fight that most unions lack the clout to wage.

Had the USWA been able to sustain its strike and force Tenneco to the bargaining table, unions in the South would have had a powerful argument in wooing both workers and facing down strike-fearing company executives. Not only would the USWA's hand have been strengthened in trying to organize companies like DuPont, with its extensive Southern operations, but the union movement as a whole could have claimed a badly needed success story. As things stand now, it's unlikely to be written in Newport News.