Horn, the U.S. president and CEO, was the automaker's public face when the scandal broke in September, calmly enduring a two-hour grilling from a congressional subcommittee.
The clashes included German executives resisting Horn's plan to give diesel owners $1,000 worth of gift cards and vouchers to buy goods at dealerships as a gesture of goodwill, said Alan Brown, head of VW's National Dealer Advisory Council.
Horn's sudden departure comes as the company faces a March 24 deadline from a federal judge to get government approval of plans to fix the polluting diesel cars.
According to Brown, Horn also differed with superiors at VW's headquarters in Wolfsburg, Germany, about vehicles to be sold in the U.S. and what prices to sell them at.
Brown said the dealer network is "hanging on by a thread," and some could file class-action lawsuits over economic damage caused by VW's conduct.
VW potentially faces more than $20 billion in U.S. fines, as well as hundreds of class-action lawsuits from angry vehicle owners.