He moved with his family to Houston in 1939, where he met Marjorie Gougenheim, whom he married in 1947.
He attended the University of Notre Dame in South Bend, Indiana, and then returned to Houston, where he became engaged in the building-materials business and then in home construction.
McConn became president of the Greater Houston Homebuilders Association in 1969, and from there became known in local politics, having been appointed to a vacant seat on the Houston City Council by then Mayor Louie Welch in 1971.
In the first round, he lost by a large margin to conservative former district attorney Frank Briscoe, but he won the runoff election due in large part to support from minority voters and endorsements from other first-round candidates.
He won reelection in 1979 against councilman Louis Macey, but lost to Kathy Whitmire in 1981.