"We remain unconvinced Chrysler will survive in its current form despite (Chief Executive Officer Sergio) Marchionne's blood, sweat and tears," Warburton said, the Detroit Free Press reported Friday.
Warburton applauded the new CEO's efforts to cut costs, but lamented the lack of new products.
Marchionne has said Chrysler, which underwent a bankruptcy process last summer, needs to sell 1.1 million vehicles in the United States and 1.65 million worldwide to break even this year.
Warburton estimated Chrysler came close to breaking even in the first quarter, but it remains the only major U.S. automaker with declining sales in the first three months of the year.
Chrysler's sales slipped 5 percent in the first quarter. Its market share has dropped sharply from 11.2 percent in the first quarter of 2009 to 9.2 percent in the most recent quarter, the newspaper said.