in the Presence of the Senate and House of Representatives

This clause is what gives Congress the ability to vote and resolve any disputes. If the Vice President has the authority to toss a vote and ask the state legislature, then he can unilaterally undo the electoral college vote as long as the state legislature agrees with him.

There also is the likelihood of an immediate challenge to the Supreme Court if the Vice President if he tried this. Someone tried suing over it, but the Supreme Court said "We won't rule on this unless it actually happens."