This phase II trial studies the safety and effectiveness of an induction chemotherapy (ACF) consisting of paclitaxel albumin-stabilized nanoparticle formulation (nab-paclitaxel), cisplatin and fluorouracil followed by chemoradiation therapy in treating patients with stage III-IV squamous cell cancer of the head and neck. ACF may be an effective way to reduce or downgrade locally aggressive tumors, and improve the chance of eradication by chemoradiation.