First of all, let's find the context in order to understand this more.
The biggest corporations don’t need another champion ... you do
Google the first part of that quote (by using quotation marks around it), and you'll get about 208 results. Open a few of them, and you'll see that Obama has reused the same phrase multiple times. After reading the context for each time the phrase was used, it becomes clear what he exactly meant.
Almost every time, Obama said it in a speech to support a Democratic candidate running for the senate. Obama was making those speeches in the "important states" in order to urge people to go out and vote for this candidate, the Democrat, as opposed to the Republican. Generally, it's believed that Republican fight for the big corps (lower taxes for the wealthy, hindering minimum wage raise, etc.), and Democrats fight for the common people (equality in marriage, affordable health care, etc.) Now that the context is clear, let's deliver this four-bagger of an answer.
Basically, Obama is saying
Vote for this Democrat candidate as he'll fight for you [be your
champion], as opposed to the Republican who will fight for the wealthy
and big corps [be their champion]. The biggest corporations already
have a lot of Republicans fighting for them, they don't need another
one [the Republican candidate in this race in this state], but you do
[you need a champion for you, who is the Democrat in this race in this
I hope that made things clear.