If it’s determined he lied it would technically invalidate everything. It automatically justifies his arrest and removal. Obamacare would not be a real law nor would any of his executive orders. He’d be undone and the rats discredited. This is why you won’t hear anything about it. If you do, it would be followed with some pretty major fireworks at a national and international level.
I Agee on constitutional grounds, but in real world it will never, ever, make a practical difference.