Under the 12th Amendment of the Constitution the Vice President, if not chosen in the National election, is chosen by the United States Senate. The House of Representatives has no authority over the Vice Presidency.
Under the second article of the 25th amendment, whenever there is a vacancy in the Vice Presidency, the President nominates a candidate and both Houses of Congress must confirm the candidate by majority vote.
This episode takes place in February 2016.
Jake Epstein (Chuck Russink) and Jeff Clarke (Congressman Kevin George) both previously starred in The Zack Files (2000). They played Cam Dunleavey and Dan Greenburg respectively.