Get number (count) of all system tweets with defined phrase within one day


Task: to develop a script with following logic:
Incoming data - 1) name of the Celebrity, 2) Date.
Outgoing data - number (count) of all tweets mentioning this Celebrity within this Date
Taking into account Twitter API limitation for number of queries per hour - is this task feasible in general? if yes - what solution exists? Will twitter streaming API help?
Thank you.