The lead assumption is that the House IT system started the theft

There were two breaches.  One involving the House IT guy who had access to Debbie's e mail and one involving the DNC break.  But, once the IT guy had Debbie's local password, it is short work to get her DNC password, and from there the hacker need only send a document to DNC under Wasserman's e mail.  The sent document would be opened and release the virus on the DNC.  This is the most plausible scenario, and it would also lead to the Podesta breach.

Rep. Debbie Wasserman Schultz, the former head of the Democratic National Committee, did not tell the DNC’s own officers about a breach on its servers for more than a month after learning about it, according to then-DNC officer Donna Brazile.Wasserman Schultz alerted the officers of the breach only when The Washington Post was about to make the revelations public, Brazile writes in an excerpt of the book Politico ran Thursday. The DNC instead enlisted the law firm of Perkins Coie to make major decisions, including how to handle the breach of its servers that led to an embarrassing email dump.