He was credited with beginning the investigations into the Teapot Dome scandal, a bribery incident that took place from 1922 until 1923, and was considered as a candidate in the 1924 and 1928 presidential elections. During the 1924 presidential election, Wyoming's six Democratic delegates were instructed to vote for Kendrick at the 1924 Democratic National Convention and did so for the first three ballots. During the 1928 presidential election, he was speculated as a possible vice presidential nominee, but the nomination was later given to Senator Minority Leader Joseph Taylor Robinson at the convention.