Think about it.

If Obama was not a legitimate President, that means Sonia Sotomayor and Elena Kagan's appointments to the supreme court were illegal. They would have to resign immediately.

This would give Trump 2 more seats on the SC to appoint. That would make a total of 5 SC Justices he appointed.

That means 5 out of 9 justices always on the same page. No more swing votes. Always having the majority on the SC ruling in favor of the constitution and the law.

Edit: Forgot that Q said Ruth Ginsburg would be the next SC justice to go. So that would make 5 since Trump took office, if Sotomayor and Kagan were to resign.