It's not the size... how many years has it been there? If it's 3 feet high and planted within the past 6 months, it's likely a child can pull it out. If it's 3 feet high, but has been growing there for a decade (and is a naturally small sized shrub), it'll take a little effort. Regardless, if you cut it and leave it to rot, it may be a decade or longer before it has rotted away completely, depending on the species. If you have a strong rope, you can tie the rope to your car and around the shrub near the base, and maybe be able to pull it out. But personally, I'd take a shovel to it first. (Well, personally, I'd just use the bucket of the tractor to lift it right out of the ground, but I assume you don't have a large tractor laying around.) While you're digging, see how much you can wiggle the thing. Once it seems fairly loose, you may be able to pull it out by hand. Or, if it's fairly loose and you can't, provided you've dug down a little bit on the side facing where you can back a car near it, you can use a rope to pull it out.
Another question - how big around in circumference is it? A rule of thumb often used for trees is if there is tree above a point, there are roots below the point. I.e., the roots radiate outward as far as the branches. So, the bigger around the bush, the more work it's likely going to take. A tap root being the wild card - those suckers can make it very hard to pull out by hand.
Another strategy - if you can pull with a vehicle in multiple directions, pull one way, disconnect the rope, reconnect and pull in a different direction. Back and forth, "rocking" the bush, and you'll likely be able to yank it out eventually with no effort with a shovel - I recently removed two large weeping cherries that were dying that way - took about 10 minutes each to yank out each tree with most of the main roots, using an F150. (Tractor needed radiator fluid.)