Say, ask around and find a friend who has a jointer, a surface planer, and a tablesaw. You'll want to get all of those 2×4s smooth square and straight for the glue-up. If any of the boards have crooks or non-straightness to them cut them shorter before jointing to remove the crook and you'll be able to lay them up once all the pieces are straight. For your purpose, gluing two smooth 2 or 4" wide surfaces together will be plenty strong without any interlocking glue joints.
I second Charles' comment about making the top surface end grain, but another option would be to cut and arrange the boards so that the top surface is quartersawn, meaning the growth rings are running vertical from the top to the bottom of the countertop. In essence, you're looking at the edge grain as your top rather than what would normally be the face grain. I think this looks better for pine and will make it look less like 2×4s. Google "quartersawn pine images" to see what I mean about the growth rings running perpendicular to the face of the board.
Edit: following up on dhazelton's comment below, the quartersawn suggestion would also help limit expansion across the width of the countertop to about 1/2 that of a flatsawn layup.