The molecular components of three giant H II regions (NGC 5461, NGC 5462, and NGC 5471) in the galaxy M101 are investigated with new observations from single-dish telescopes (James Clerk Maxwell Telescope and the NRAO 12 m) and from the Owens Valley Radio Observatory millimeter array. Of the three H II regions, only NGC 5461 had previously been detected in CO emission. We calculate preliminary values for the molecular mass of the GMCs in NGC 5461 by assuming a CO-to-H₂ factor (X factor) and then comparing these values with the virial masses. We found that the appropriate X factor is 5 times smaller than the X factor in the Milky Way despite the lower metallicity of M101. We conclude that the data in this paper demonstrate for the first time that the value of X may decrease in regions with intense star formation. The molecular mass for the association of clouds in NGC 5461 is approximately 3 × 10⁷ M and is accompanied by 1-2 times as much atomic mass. The observed CO emission in NGC 5461 is an order of magnitude stronger than in NGC 5462, but it was not possible to detect molecular gas toward NGC 5471 with the James Clerk Maxwell Telescope. An even larger ratio of atomic to molecular gas in NGC 5471 was observed, which might be attributed to efficient conversion of molecular to atomic gas. The masses of the individual clouds in NGC 5461, which are gravitationally bound, cover a range of (2-8) × 10⁵ M, comparable with the masses of Galactic giant molecular clouds. Higher star-forming efficiencies, and not massive clouds, appear to be the prerequisite for the formation of the large number of stars whose radiation is required to produce the giant H II regions in M101.