Who is ‘another champion’ in President’ Obama’s speech "The biggest corporation don't need another champion. You do."

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 state]

I hope that made things clear.

Champion is used with the following meaning, suggesting that ordinary people, not big corps, need more support for their issues: (from TFD)

• an ardent defender or supporter of a cause or another person: a champion of the homeless.

• a person who fights for or defends any person or cause: a champion of the oppressed.