First, is the problem of cartridge length, which dictates how much movement the bolt makes to extract a spent casing and then to load a fresh round. The 9mm pistol has to move 19mm back and forth to complete the firing cycle: An AR-15 rifle of 5.56 caliber has to move 45mm. To further document the point a MAC10 sub-machinegun firing 45ACP has a RPM of 1090: the 9mm version has a RPM of 1200, and the even shorter 0.380 cal MAC11 has a RPM of 1500.
The documented cyclic fire rate of a 5.56 caliber M16 military rifle is 750. I had to search for a pistol cyclic rate which I found for the full auto Baretta 93R: 700. The M16 is slightly faster but hardly three times. At the same time I am using cyclic fire rate which is impossible to achieve. The M16 in semi-auto mod can possibly empty two 30 rd mags in a minute for an achievable rate of fire of 60. To achieve the Senator's pistol rate of 20 (1/3) with my 9mm I would need just one mag change and not empty the second mag. Thus comes the real issue which is magazine size.
Then the senator makes a remark of some mythical- high lethality- ammunition for the AR15. This in stark contrast to the fifty plus years of ex-military personnel remarking on the 5.56 rd poor hitting power. It could be he is talking about the recently Army deployed M855A1 EPR ammunition which I doubt can be purchased legally. So poor has been the 5.56mm the Army is finally changing to a 6.8mm rd bringing its size halfway back to the 7.62 NATO rd used prior. But no one is claiming the 7.62 NATO as highly lethal.