Certainly not months for a first-time offense.
That depends on the state. Go to that website and see the penalties. Montana is one of the states where the judge can sentence you to prison for months for a first time offense.
However, quibbling with drunk driving laws is not my point. My point was that, when there is a profit motive to jailing people, politicians can be influenced to pass laws that help get people jailed and that shouldn’t be allowed.