National Trails System Willing Seller Act - Amends the National Trails System Act to: (1) prohibit the federal acquisition of lands outside the exterior boundaries of any federally administered area, except with the owner's consent, for the Oregon, Mormon Pioneer, Lewis and Clark, Iditarod, and Nez Perce National Historic Trails and the Continental Divide, North Country, Ice Age, and Potomac Heritage National Scenic Trails; and (2) provide that federal authority to acquire fee title shall be limited to an average of not more than one-quarter mile on either side of such national historic trails and the Continental Divide National Scenic Trail.