Lyndon Johnson won the 1964 presidential election defeating Barry Goldwater. In the 1964 presidential election the popular vote totals were Johnson 43,129,566 and Goldwater 27,178,188.
The largest percentage of popular votes in a presidential election were won by Lyndon Johnson 61.05% in 1964, Franklin Roosevelt 60.80% in 1936, Richard Nixon 60.67% in 1972, and Warren Harding 60.32% in 1920.
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Yes, in the 1964 election he received 60% of the popular vote, a record unless you count the 1820 election when there wasn't an opponent to the imcumbent President.