Do socially paired songbirds need to copulate daily because only one egg is laid each day?  How long does it take from the point of first copulation to the laying of the first egg?  Can the female influence this, i.e. if she mates 3 days before her nest is ready vs 6 days before it's ready, is the sperm stored/egg production delayed?

In short, no, they do not need to copulate daily. Birds, like many animals have the capability to store sperm, allowing them to delay fertilization. I can't say how much the female can influence this, although I am sure there is tremendous variation between species, as is the time between copulation and laying of the first egg.

In some cases, the number of eggs laid makes a difference. I read a study a long time ago (sorry, I have completely forgotten the reference for it) in which the researchers studied a bird that generally laid three eggs, one a day. Each day, the researchers took an egg out of the nest, leaving one. One poor bird laid something like 70 eggs before she finally gave up. I can only imagine the bird was eating like crazy to make up for all the resources going to waste making all those eggs. In answer to your question, the bird had only copulated once before laying the first egg and did not copulate after that.