Nope, let them go ahead with the whole investigating thing!
If he resigns now, everyone will breathe a collective sigh of relief and things will somehow ... settle down and sort themselves out.
However, Pence is not only a vile near-fundamentalist religious conservative, he was also Trump's transition lead. Unless Trump is himself in the clear, which seems increasingly unlikely, Pence is either complicit or completely incompetent. They both need to go down, so I'm afraid The Donald will have to cling on until there's enough evidence to get rid of Pence, too!