when a noun is used with нет, it is always in the Genitive case.
Время and имя belong to a small class of neuter nouns that all end in -мя and have additional -ен in all oblique forms. This class only has ten nouns (roughly in the order of decreasing popularity: имя, время, племя, пламя? знамя, семя, бремя, стремя, вымя, темя).
Here are some examples
У меня есть виза. У меня нет визы. I have a visa. I do not have a visa.
У тебя есть лампа. У тебя нет лампы. Do you have a lamp. You have no lamp.
У него есть машина. У него нет машины. He has a car. He has no car.
У неё есть работа. У неё нет работы. She has a job. She does not work.
У нас есть семья. У нас нет семьи. We have a family. We have no family.
У вас есть идея. У вас нет идеи. Do you have an idea. You have no idea.
У них есть проблема. У них нет проблемы. They have a problem. They have no problem.
У нас есть дверь. У нас нет двери. We have a door. We do not have doors.
"I don't have the time" might give the impression that you're being asked what time it is.
Here, "Do you have the time" is used to ask someone what time it is. "I don't have the time" would be an appropriate response to the question, as Dejo stated. Using it the other way may not be technically wrong (I'm not entirely sure) but it definitely sounds weird, regardless. I wouldn't use it that way if you can avoid it.
In my part of the English-speaking world, if we are asking someone to tell us the time we usually ask, "What time is it?" Or, "Do you know what time it is?" If we overhear someone say, "I don't have the time," and he's a local, it would mean he's too busy to help with something. It's just our dialect. If we understood him to mean by this that he didn't know what time it is, we would know he's not a local but rather from some other part of the world. I'm in the midwestern USA.
Oh no, we usually say "what time is it" instead of "do you have the time," but it IS said by some, and is more of a formal version. But anyone I've ever heard has said "I don't have time" if they don't have time for something, whereas they'd say "I don't have the time" if they didn't know what time it is. Granted, that response isn't said much in general, since most people won't ask "do you have the time" in the first place. It might be a regional thing if people respond that way. I'm from Texas, by the way.