The Vice President can assist with the passing of laws even though he is part of the executive branch. There are some things he can do to help laws get passed or defeated.
One thing the Vice President can do is break a tie vote in the Senate. If there is a tie in the Senate when a vote is taken, the Vice President casts the deciding vote. Thus, his vote will determine if a law passes or not when there is a tie.
Another thing the Vice President can do is lobby members of Congress. He can meet with members of both houses of Congress to explain why a bill should or shouldn’t be passed. Many times the advice, insights, and urging of the Vice President can help persuade a member of Congress to vote a certain way. The Vice President can play an important role in the legislative process.