It's the same as for any government employee. First, obviously, the law. It's not actually within his power to just write something down and sign it to make it

It's the same as for any government employee. First, obviously, the law. It's not actually within his power to just write something down and sign it to make it the law of the land. There's a process that has to be followed, of which the comment period is but one step. Regulatory decisions are also required to, in general terms, make sense and be fair. The new EPA head is currently coming to the realisation that there are limits to his power, especially when he's trying to change rules which had just recently been created: quickly flip-flopping on regulatory issues is an open invitation to be sued by, for example, companies that have based decisions on the assumption of regulatory stability. It's also really hard to argue convincingly to abolish a rule, when the almost unchanged group of people has just made the convincing case for that rule a year ago. But beyond those squabbles, he is accountable to the people who hire and fire people in his position: the President and Congress. The assumption being that people realise it is the Republican Party who deserves the blame for this disaster of an idea.