In our English grammar book, It always takes this fixed pattern: It is [high] time that somebody did/should do something. The predicator of the subordinate clause takes either 'past tense' or 'should plus the base form of a verb .' From above two gentlemen's answers, we know that the predicator of the subordinate clause takes the base form of a verb with 'should' omitted in America.

What exactly do you mean by past tense clause here? In my experience, "it's high time" (or "it's high time that"... no difference) is usually followed by the subjunctive, i.e. "It's high time we get going," "it's high time that we take a picture," or, less frequently, the past subjunctive, i.e. "it's high time we were going," "it's high time that we were more serious." While the subjunctive mood isn't used as often in English as it is in the romance languages, there are many phrases that use it. Usually, it follows a wish, thought, or command and is introduced by the word "that," i.e., "it is important that you be here tomorrow," "i suggest that you be quiet," or, past-wise, situations where an element of uncertainty is present, i.e., "if it weren't for him, we'd be there by now," "it's not as if i were lost," "i wish i were home," "if only I were a little bit taller," etc. In this latter case, the subjunctive verb tense is typically introduced by "if." Let me know if this is what you were referring to.

You have "have to" use past tense clause following that phrase; I think that's just what's most commonly used. For example, you could say "It's high time we get this place in shape" and it would make sense.