He was a delegate to the 1860 Democratic National Convention at Charleston, South Carolina.
In 1860, he ran for Canal Commissioner on the Douglas Democratic ticket, but was defeated by Republican Samuel H. Barnes.
Barnes died a week after the election, and the vacancy was filled temporarily by the New York State Legislature in January 1861.
Wright was the Democratic candidate, but was defeated by Republican Benjamin F. Bruce.
In November 1861 he ran again, for the remaining two years of Barnes's term, and this time was elected defeating Bruce and War Democrat Frederick A. Tallmadge.