1) It's illegal: Since there are currently no work permits for illegal aliens, handing them out would require a change in the existing law. If this were a dictatorship like North Korea or Cuba, Dear Leader Barack Obama could simply issue a decree and change the law. Here in America we're a republic which means that he unquestionably, uncontroversially cannot issue work permits for illegal aliens without a bill passing through Congress. His attempt to do so may seem like a small matter to some people, but it sets an extremely dangerous precedent that undermines democracy in our country.
2) Refusing to enforce the existing law sets a terrible precedent: As Obama himself has admitted, he "swore an oath to uphold the laws on the books." He is breaking that oath to try to give amnesty to illegals. Imagine the chaos that will reign if this becomes standard practice. Suppose Mitt Romney wins. Could he end the death tax or corporate taxes by telling the IRS not to enforce them? What about putting an end to hate crime laws or the endangered species act by simple choosing not to enforce them? This is the can of worms Barack Obama is ripping wide open with his imperial decree.
3) This is a temporary solution designed to be a permanent fix: Barack Obama is asking illegal aliens to sign up and apply for work permits. However, since his policy doesn't have the force of law behind it, if Mitt Romney's elected, he could hand those same applications to ICE for use in tracking down illegals to be deported. In fact, that's exactly what Mitt Romney should do (Good luck with getting him to do it) since illegal aliens are by definition breaking the law and the penalty is deportation. In any case, the American people and businesses cannot effectively make long-term decisions based on important policies that can change the second a new party gets into power. Replacing laws with illegal presidential decrees creates instability and unreliability that makes for bad policy that helps paralyze the country.