Very little, if any.
Most of the people who want out won't qualify. Canada is quite a difficult country to move to. Of those who do, many will not actually take the step to leave.
If a large number of highly skilled people apply, then EE points requirements may go up (because if thousands of PhD holding Americans join the pool, they can get the same number of people with higher point thresholds).
If there's a sudden influx of spousal support applications, American apps may start needing a higher burden of proof, as is required from most of the world.