Johnson ran against Governor Orval Eugene Faubus in the Democratic Party primary in 1956. Johnson accused the segregationist Faubus of working behind the scenes for racial integration. Johnson finished second with 83,856 votes (26.9 percent).
Johnson also played a role in the Little Rock Nine crisis. He was elected to the Arkansas Supreme Court in 1959 and served until 1966.
In 1966, Johnson won the Democratic gubernatorial runoff primary, 210,543 ballots (51.9 percent) to fellow Supreme Court Justice Frank Holt's 195,442 votes (48.1 percent). Johnson then lost the general election, 257,203 votes (45.6 percent) to the moderate Republican Winthrop Rockefeller's 306,324 (54.4 percent). Johnson won majorities in forty counties to Rockefeller's thirty-five counties. Every major population center supported Rockefeller, who prevailed in the northwestern counties, in Little Rock, and in many eastern counties with large African American populations. Black voters provided Rockefeller's margin of victory.
Johnson ran against J. William Fulbright in the Democratic primary 1968 but was again defeated. His wife, Virginia Johnson, meanwhile, ran for the governorship in the same primary election, making her the first woman in Arkansas to run for governor, but lost the nomination by a wide margin to State Representative Marion H. Crank (1915–1994) of Foreman in Little River County, who was in turn defeated by Rockefeller in the general election.
Johnson had a long-standing enmity with Bill Clinton. While he had been a student at Georgetown University in Washington, D.C., Clinton was a campaign aide for Johnson's 1966 runoff opponent, Judge Frank Holt. Twelve years later, Clinton would win the governorship. Clinton once remarked to Johnson, "You make me ashamed to be from Arkansas.
During the Whitewater scandal, Johnson made accusations against President Bill Clinton, based on a continuing opposition research campaign against the Clintons conducted by Republican political consultants, Floyd Brown and David Bossie. A client of Johnson's, David Hale, a former municipal court judge, was the special prosecutor's chief witness attempting to link Clinton to the Whitewater scandal. Hale's testimony was deemed to be of no import, as he had agreed to testify to receive a better plea deal on his own indictment for fraud charges.