Volunteers: Assignments with impossible deadlines or pointless pet-projects work best when asking for volunteers. Offer nebulous rewards with as few specifics as possible like “an appropriate amount of comp-time”, or “the thanks of upper management”, or the ultimate, vague non-reward, “a chance to work on elite company-critical research projects in the future”.
If no one volunteers, assign it to the team-member least qualified to handle the project, or failing that, the least paid. After struggling alone, the novice employee will eventually have to ask for help from your more senior team members. Such a debacle will assure that your most qualified employees will voluteer in the future for such projects, knowing that inevitablly it will be fall on their shoulders anyway.