The short answer is "no." There's no contemporary mention of the curse. The legend surrounding the Curse of Tippecanoe is often contradictory, with some versions attributing to Tecumseh after the Battle of Tippecanoe (occasionally and erroneously placing Tecumseh at the battle itself) or as he was dying in the Battle of the Thames in 1812; alternatively its Tenskwatawa who gets the credit after either of these events. The Curse may be an early 20th Century invention; I've yet to see anyone trace it back further than Ripley's Believe It or Not in the 1930s.

Going back a century earlier, Tenskwatawa was interviewed by C.C. Trowbridge, well after Tecumseh's death. Though they do discuss the spiritual powers of Shawnee holy men, the Curse of Tippecanoe is not mentioned here. However, what Tenskwatawa does say about the nature of Shawnee spirituality makes the idea of such a curse unlikely.

First, using spiritual powers to harm another is regarded as a great evil, and something that Tenskwatawa himself campaigned adamantly against (resulting in the Shawnee witchhunts in the early 1800s). Using his powers to harm others would risk his eternal soul, potentially isolating him from blissful afterlife he envisioned (Tenskwatawa's "heaven" and "hell" weren't as cut off from each other as the Christian versions, and had pathways linking them that those who had been redeemed through great suffering in the afterlife could travel, but the irredeemable would just be snuffed out of existence). Additionally, the way curses traditionally worked were more immediately and visceral. You don't kill someone by making vague pronouncements into the ether. The curse is embodied in a small physical object which the person making the curse causes to fly off and embed itself within the target of the curse. The target feels a prick, begins to feel ill the next morning, and dies a few days later. It doesn't linger for decades, and it can't target people who aren't even born yet.

Finally, even if Tenskwatawa was both willing and able to perform a multi-generational curse on the office of the President, he would have seen little use in it. His movement was millenarian; the end of the world as we knew it was drawing swiftly near. The task of Native peoples was not to drive off Euro-Americans, but to resist and endure them until the fateful day when they'd either be swept off the continent or converted / adopted into Native societies by grand cosmic forces.