I am having trouble with my landlord and refused to pay rent this month because he will not fix nothing. He sent a letter for demand to pay or get out. We found another house and want to move but it will not be ready until April 7th or so, can he evict us before we can get into our new place.

Most states it takes a 30 day notice.
I have heard of three day notices though.
It depends on your state law.
What state are you in?

How many day notice was your "pay or quit" notice, after that, he will file for a formal eviction, depending on the court schedule, it can be within a week to two weeks to get a court date, at court they will normaly give you 3 days to one week.

So my guess is 2 weeks a the fastest to about 3 weeks to get you moved out by force.

Now do understand you will still owe him the rent, and he will then file for a judgement against you for the rent owed. One can not just no pay because of repairs, there is legal requriements to do it, putting it in escrow, filing a suit for repairs and more.