He is responsible for pushing policy and passing laws. He needs to be able to have strong deductive reasoning skills as a matter of principle. He isn't just someone sitting there throwing around accusations off of an armchair. He holds the most powerful office in the world. Voter I.D. laws have been claimed by conservatives to help conservatives because they disproportionately impact the poor. For the president to say "Illegal voting is out of control! We need to pass voter I.D. laws!" and if the those laws actually get passed based on wild speculation is extremely reckless - not to mention a huge waste of resources. 

I'm kind of shocked someone with your background thinks policy should be enacted based on speculation.

Any audits of voting by Republicans or Democrats does not point to rampant voter fraud in the millions. 

It's nobody's job to prove a negative - it's his job to back up his reasoning before calling for policy changes.