Halfway through the speech Charlie’s throat gets dry & begins to crack (probably from nerves) and he pauses and asks for water. In his autobiography, Charlie recalled that a glass could not be found, so water was brought to him in an envelope.1
|Charlie & Mickey Rooney, who also performed, talk to First Lady Eleanor Roosevelt|
at the inaugural gala which was held the evening before the swearing-in ceremony
(which Charlie also attended).
1 Contemporary newspaper articles (as well as the announcer in the clip) say that master of ceremonies, Douglas Fairbanks, Jr., brought Charlie a "glass" of water.