Campaigning in Texas, McCain mocked Obama for suggesting that he would send troops back into Iraq "if Al Qaeda is forming a base there," as debate moderator Tim Russert put it.

In the clause 'as debate moderator Tim Russert put it' , what is it that Russert put? About McCain's mocking or Obama's suggestion?

The way that someone "puts it" means the way that he says it -- the actual words that he chose.

The reference is to the quote. How did Russert put it? Here's how he put it: "if Al Qaeda is forming a base there". Those were the words he used.
So it is not unusual after quoted material to see as he put it. In such cases there is a desire to call attention to the exact words to point out that they are unusual words or words that express something very unusual or perhaps even false.
I don't know how to put it. = I don't know how to say it. = I am having trouble finding the right words to express what I want to say.

put it: formulated it, said it
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I understand how 'put it' used more clearly. Thank you, CalifJim.Emotion: big smile
 Marius Hancu's reply was promoted to an answer.
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