Huge difference among tub makers, and even among dealers. I am fortunate enough to live close to the factory, and I sell HotSpring - who can have a tub ready to pick up just 48 hours after I order it - but our delivery schedule is about two weeks out right now.
HS dealers who are farther away from the factory stock tubs in a warehouse and can get the thing to you in a couple of days if they have the color you want on hand and the delivery schedule allows.
I get calls from manufacturers just about every week asking me to consider selling their products: the last one was in Florida, and said they could "guaranty" just four weeks from order date. They were very proud, saying that was faster than most others in the industry.