As a result of his anti-slavery views Jenkins became a Republican when the party was founded. In 1856 he served as delegate to the first Republican National Convention. In 1857 he was the unsuccessful Republican nominee for a seat on the New York Court of Appeals, losing to Hiram Denio. In 1858 he was a candidate for the Republican nomination for Governor of New York, and lost to Edwin D. Morgan, who went on to win the general election.