So yes and at the time same time no. The most prominent moral critics came from Protestant evangelical clergy and women, most notably Jeremiah Evarts the corresponding secretary for the American board of Commissioners for Foreign Missions. Evart organized protest meetings, petitions, and wrote under a pen name in major newspapers. Catherine Beecher (of the famous Beecher family) lead the women's opposition to reform largely using petitions. More creative opposition came in the form of plays sympathetic to the blight of the Native Americans.
In Congress the evangelical senator from New Jersey, Theodore Frelinghuysen, lead the charge initially against the Jacksonian administration. Frelinghuysen's dramatic speeches earned him the nickname the "the Christian statesman". However for the most part there wasn't much moral opposition from national politicians like Henry Clay (who didn't show much concern for Natives during his career until this point) although there are certainly notable exceptions like Davy Crockett. It wasn't until the moral campaign of the women and the evangelicals took off that the National Republicans fully mobilized to oppose Indian removal. This opposition was however more of a challenge to Jackson than any moral opposition to Indian removal, for most politicians at least.