Our Government could easily expose the fact (if it is a fact). Elect a Republican majority to Congress and have thenm subpoena the birth records from Hawaii. Our courts won't touch this issue, just as they wouldn't rule on the constitutionality of the Vietnam war. Not out of cowardice (in either case), but because they are sensitive to the fact that they are the only unelected branch of Government, and because they are constrained by 220 years of precedent as to the limits of their jurisdiction.
I imagine we will elect a majority Republican Congress next and that Dear Leader and his Czars will spend another 5 trillion dollars between now and then.
But they have never had in 220 years to deal with an usurper in office who effectively is using the race card to silence everybody, even the Clintons who were the first "birthers"???
It SHOULD be their forum to settle this Constitutional crisis, a crisis that our nation has never experienced before, whether we like it or not, or if it unpopular, The Constitution is the Constitution that SCOTUS deals with every day!!!