When the Supreme Court basically agreed with the Cherokee that they should be allowed to stay on their lands and not be removed by the federal or state governments, Jackson supposedly said that "[Chief Justice] Marshall has made his ruling - now let him enforce it." He refused to back up the SC ruling, even though enforcing federal law and court rulings is a major part of the Chief Executive's job, and was thus grounds for impeachment. Nothing happened in Congress, of course, because most white Southerners agreed with Jackson and wanted the Native Americans gone, partly out of racism, and partly so they could take their lands for themselves. It's worth noting that Jackson is apparently one of Trump's favorite US Presidents, and he has a portrait of Jackson hanging in or near the Oval Office. He does, however, completely lack Jackson's raw guts, or military experience. He does have Jackson's bigotry, pettiness and vindictiveness, and racism down pat, though.
ETA: Jackson also introduced the Spoils System, which resulted in much of the political corruption of the mid-to-late 1800s. Not unlike Trump today.