OK, for decades, the term "tarp" referred to cotton duck canvas known as "tarpaulin".
It was very thick woven fabric, usually treated with some kind of wax or other waterproofing.
Even without the waterproofing, if it was sloped, it was fairly waterproof because the water just ran off the thick weave.
I have slept under a tarpaulin lean-to in the river swamp hundreds of times in driving rains.
And, to tell the truth, if treated, they are excellent vehicle covers, because they will let moisture escape.
But, they can also sometimes cause them to rust by trapping the moisture against the metal.
But, if they are kept off the metal they work well.
Unfortunately, they are getting hard to find. They are still being made, and military surplus often has them.
I don't know when the Wally World cheap plastic thingys started coming out and being called tarps, but they are a disgrace to the name.
Having said that, I have used lots of them, and they have their place for very temporary use.
But they will not stand up to sunlight for long. You can spray them with Armor All every so often, and they will last a lot longer.......
But, there is something out there that will stand up to the sun, is totally waterproof, and will last for years and years.
Its vinyl coated polyester.
I have a green one, that I bought from a local place that makes them to spec.
I bought it to go over a grain trailer I was using to store deer feed. It stayed over that trailer, in the full Fl. sun, for 5 years.
Then, I sold the trailer, and put the piece over some other stuff.
Right now, it is over a friend's popup camper stopping a leak around the air conditioner until we get a chance to fix it.
So far, it has spent most of its life in the sun and weather. I bought it in 1988, and its in as good a shape as when I bought it except for a few scrapes and stains.
This is the place I got mine.
http://cpdothan.com/truckcoverings.htm
Its about 30 minutes from my farm, so I just rode up and ordered what I wanted. I have bought several different ones from them since for different things.
I don't recommend ordering from them, since they are so far away. I'm sure you can find a local place.
The thickness is rated in oz per square yard.
Lots of places sell 18 oz stuff. It works, and is tough. I buy only 22 oz stuff. At the place I buy it, its only a couple of bucks more expensive per tarp, and it stands up to a lot more abuse than the lighter stuff.
My place will make me a tarp of even heavier stuff. I was going to get one, but they showed me a small one made out of it.
It was great. Darn near bulletproof. But it was just too heavy and stiff. My 22oz ones are a handful, and I would hate to try to pull some of this over a trailer or anything irregular.
Check the yellow pages for tarps or truck tarps. Be careful, truck tarps are often just a mesh to hold stuff down and are not really waterproof.
Farm supply places might sell the good stuff, or might know who does.
I know you don't want to spend much on a temp solution, but one of these tarps is useful year round, and will continue to be useful after you get the shed built.