Phelps was elected to the Missouri House of Representatives from the Kansas City area in 1960 and was re-elected five times. In 1972, he was elected Lieutenant Governor of Missouri and was re-elected in 1976. Phelps campaigned on a pledge to be Missouri's first "full time" Lieutenant Governor and upon his election to that office, he gave up the practice of law. In 1980 Phelps was an unsuccessful candidate for the Republican nomination for Governor of Missouri. He lost the Republican primary election to former Governor Kit Bond.
After a sixteen-year absence from public life, in 1996 Phelps ran for Congress in Missouri's 4th congressional district. Phelps won the primary, but was defeated in November by the incumbent, Ike Skelton. Phelps currently works as the national spokesman for Americans for Fair Tax, a group that advocates replacing the income tax with a national sales tax.