PART 2: Patients receive alvocidib IV over 1 hour at or below the MTD determined in part 1 and then receive a maintenance dose of alvocidib IV over 1-6 hours on days 1, 8, and 15. Cohorts of 3-6 patients receive escalating durations of the maintenance dose of alvocidib until the MTD* is determined. An additional cohort of 10-20 patients receives alvocidib over 1 hour on days 1 and 15 at the MTD.