Connors graduated from Forest Park High School in Cincinnati, Ohio in 1975 and earned his bachelor's degree in marketing communications at the University of Alabama in 1979. He was hired as executive director of the Alabama Republican Party in 1985, just as Republicans, with Ronald Reagan at the head of the ticket, were beginning to break up the Democrat-controlled "Solid South".
Connors campaigned in the 1992 Republican primary for the 6th Congressional District of Alabama seat held by Democrat Ben Erdreich. He lost a primary run-off to Spencer Bachus, who went on to defeat Erdreich for the seat. Connors completed a fellowship in modern political communications at Harvard University's John F. Kennedy Institute of Politics in 1993.
Connors was named chair of the Alabama Republican Executive Committee in 2000, and served for just over five years. During that time he helped raised funds to litigate against the Alabama State Legislature's 2001 redistricting plan. He also spearheaded Republican Party efforts to oppose Governor Bob Riley's proposed "Amendment One" tax reform plan. The defeat of that referendum was cited by the American Conservative Union when it presented Connors with its "Ronald Reagan Award" at the Conservative Political Action Conference in January 2004. Connors was succeeded as chair in February 2005 by Twinkle Cavanaugh.
In 2007 Connors served on the Alabama Statewide Finance Committee for Mitt Romney's presidential campaign. Since then he has worked as an independent political consultant with his M. J. Connors Consulting.
In April 2018 Connors and Alabama House District 47 Representative Jack Williams were arrested by federal agents and charged with conspiracy and fraud relating to California-based Trina Healthcare's efforts to influence Alabama law.