The Minnesota AFL-CIO yesterday endorsed millionaire businessman Robert Short for the four years remaining in the term of the late senator Hubert H. Humphrey.

Though the endorsement was pushed by state and national AFL-CIO leaders, it was not easily won or enthusiastically given. Short needed 433 of 629 delegate votes to win the endorsement. He got 474.

His success came in part because of commitments he made to individual unions during meetings Monday and Tuesday, pressure applied on his behalf by some international unions and an enthusiastic personal endorsement Tuesday by Vice President Mondale.

Even so, in a hour-long floor fight before the vote, several delegates were openly hostile toward Short who defeated Liberal Democratic Rep. Donald M. Fraser in the Sept. 12 primary. Fraser has been endorsed by Minnesota's Democrat-Farmer-Labor Party and the state ALF-CIO.

Short financed his primary campaign with $750,000 of his own, and campaigned largely on his opposition to abortion, his support of unrestricted use of the Boundary Waters Canoe Area in northern Minnesota and his pledge to cut $100 billion in federal spending.

The central committee of the Minnesota DFL Party has not endorsed him.

At the convention in Duluth, public employes, teachers and machinists, among the more liberal members of the AFL-CIO, objected most strenuously to the endorsement. They particularly criticized Short's allegedly anti-union record as an employer and his campaign tactics.

We have had considerable dealings with Short and we've had problems all the way," said Robert Jensen of the painters' union in Minneapolis.

Al Church, a leader of the public employes union in Minnesota, remarked. "Some of my brothers and sisters must have cast-iron stomachs if they can swallow Short after the dirty, low-level, irresponsible campaign he just conducted."

Despite this rank-and-file animosity, Short was strongly supported by state and national AFL-CIO leaders because of his promises to vote on labor's side on such issues as labor law reform, Hatch Act reform and common-site picketing.

Virgil Miller, international vice president of the American Federation of Government Employes, pleaded with the convention to endorse Short. "Please send us someone to Washington whom we can work with," he said.