I pray with Chassidim. Before someone begins to lead the prayer, they ask if he underwent ritual immersion that morning.
Is there a (and if so, what is the) source for this requiring the cantor to have immersed?
The Lubavitcher Rabbi Zatzal Igros Kodesh 11:401 explained the purpose of Tevila in the Mikva in the morning is based on the Rashba which is mentioned in the Magen Avraham 4 that when one prays he is like the Kohain who is doing the Avoda, and the Kohain always does a Tevila prior to doing the Avoda.
However since it is too difficult (אין כח בצבור לעמוד בה) therefore it is not enforced only in general.
Perhaps based on this there are some Shuls that require a Chazan to go to the Mikva prior to Tefila.
See also Likutei Torah - Parshas Ki Savo - end of page 43 where it mentions that everyone agrees that Tefila is more accepted with a Tevila prior to it.