I can't seem to find any good information on this topic. I figured that since the United States had a pretty good record on free speech, there must have been some citizens who objected to the Indian Wars, much like the protests that occurred during the Mexican War and the Civil War.
Yes, there were citizens who objected to the various removals & attacks against the Native Americans including the Supreme Court of the United States in Worcester v Georgia.
Many abolitionists also fought Indian Removal & Genocide because from the abolitionist perspective, the land might become another slave state.
As for the 'free press,' a good book that combines your interest in dissent (including dissent against the genocide of Native Americans) & the press might be Juan Gonzalez & Joe Torres' "News for All the People." A short version is: if white people didn't like what your press was publishing, they would come, destroyed the press, and attempted to kill the publisher.