For seven years, Meyer was the Republican chairman of Dallas County; under his tenure the county became heavily Republican in orientation for two decades but reverted to Democratic majority strength in 2006. In 1972, Meyer was the campaign manager in the long-shot race waged by Alan Steelman, a young Republican who unseated Earle Cabell as U.S. representative for Texas's 3rd congressional district, a post once held by the earlier Republican Bruce Alger. Cabell was also a former mayor of Dallas. Steelman,. however, gave up the seat in 1976 in a losing bid against Democratic U.S. Senator Lloyd M. Bentsen. In 1984, Meyer as chairman of the host committee worked to bring the Republican National Convention to Dallas. He lost a nonpartisan race himself in 1987 for mayor of Dallas to the Democrat Annette Strauss but became state chairman the next year for the first of three two-year terms. He helped Vice President George Bush win the presidency over Michael Dukakis, with their old mutual rival, Lloyd Bentsen, seeking to succeed Bush as vice president but losing out to Republican nominee Dan Quayle. Himself considered a Moderate Republican, Meyer sterred clear of primary rivalries but supported his party nominees across the spectrum in each general election. One of Meyer's successors as state chairman, Susan Weddington of San Antonio, by contrast supported conservative State RepresentativeJohn Shields in his unsuccessful challenge in 2002 to incumbent Jeff Wentworth for the District 25 seat in the Texas State Senate. Weddington opposed Wentworth's support for abortion. From 1972 forward, Meyer was a delegate to all Republican state conventions held every even year. For nine months, he headed the Victory 2000 Committee in Washington, D.C.; his work paid off with the election of the second President Bush. Former Republican state chairman Steve Munisteri, who served from 2010 to 2015, said that Meyer "had an excellent reputation for building up the party’s infrastructure and taking care of the nuts and bolts of the political operations.". Dan Branch, a former member of the Texas House of Representatives from Dallas County recalled Meyer as "a tireless fundraiser and a tireless worker." Karen Hughes, the George W. Bush political operative and counsellor, described Meyer as "a mentor for me and a key influence in my life... Fred’s leadership was absolutely instrumental in making Texas the Republican stronghold that it is." Jeanne Johnson Phillips, an oil company executive, said that she even postponed her wedding for a week to accommodate Meyer's fund-raising goals.
Family and death
Meyer was married to the former Barbara L. Spreuer, a native of Fort Wayne, Indiana, and a graduate of Indiana University in Indianapolis, who was a former personnel director for a grocerychain. The Meyers had three children, daughters Cheryl Lynn Bouldin and Amy Meyer Barrentine, and son Bradley Allen "Brad" Meyer. Bradley died in Dallas at the age of forty-eight, six months after he was diagnosed with metastasized melanoma cancer. A graduate of the University of Texas at Austin, he was engaged in the entertainment industry and was the president from 1990 to 2005 of Star Tickets in Austin. Meyer died of cancer in Dallas at the age of eighty-four. He, his wife, and son were Presbyterians and are in-urned in the columbarium of the Preston Hollow Presbyterian Church in Dallas.