If he jumps from the "51" ship to the "49" ship, then it's a "50-50" ship and the original "51" ship (D) just turned into a "49" ship and the original "49" (R) ship just turned into a "51" ship with the Veep's tie braking vote!
Still, it's a bucket of worms - the House is on the other side of him, and it seems there are more spineless Rs than Ds, so in partisan battles, the Ds would win anyway.