"God forbid ___" is a way of saying "Please don't let ___ happen" or "I hope ___ doesn't happen". You can use this for things that you really don't want to happen:
Please remember to take your phone with you. God forbid something bad happens to you and you can't contact us.
However, there's another popular use of "God forbid". People often say this sarcastically, to talk about something that they really do want to happen, but which doesn't seem likely to happen. For example:
God forbid you get off the couch and help out around here! (talking to your lazy child)
We're having Thanksgiving at Millie's again this year, huh? God forbid we ever mix it up a little and have it at someone else's house.
When you use "God forbid" in this way, you sound angry and resentful. This is the way that the speaker used "God forbid" in the example at top.
Grammatically, notice that the part which follows "God forbid" is always in the simple present tense:
God forbid we go
God forbid something happens
God forbid we have it
You might also hear this phrase with "should":
God forbid we should go a single day without it raining.
The meaning is the same with "should" or without it.