What does "put someone back into something" mean here?

Question

This was one of the moments that turned it around and put her(Hillary Clinton) back into the race against Obama in 2008.

I found the meaning below for put your back into something:

• to use a lot of physical effort to try to do something

But still I cann't understand meaning of the sentence.And I don't know if "putting back into the race" is a handicap or an advantage for her(Hillary Clinton).

So could you please explain it to me?

The fuller text:

SGC: In that moment, President Obama crying— would that moment have been different if he were a female president? Is there something different about when you see a man break down that way and a female leader of that stature break down that way?

GM: I mean, surely, without a doubt. The criticism that someone is too emotional is one of the classic gendered tropes that are used to go after female leaders. It’s worth noting that when Hillary Clinton cried a little bit in 2008 in New Hampshire it was highlighted as one of the high points of her campaign. This was one of the moments that turned it around and put her back into the race against Obama in 2008. But it’s illustrative that one of the criticisms of Hillary is that she’s robotic. Right? So that was a breakthrough of that facade.

Answer 1

This was one of the moments that turned it around and put her back into the race against Obama in 2008.

The sentence also says that this moment "turned it around", which means to reverse or undo something. So when it says this also "put her back into the race" it suggests that she had previously been taken out of the race.

This has nothing to do with a person's literal back as in the other idiom you found "to put your back into something" (which means to do something with great effort). The meaning of the word "back" here is to return.

Of course, this isn't a literal race... when people are competing in some way it is often likened, metaphorically, to a race. All contenders in a race have a chance of winning. When someone is unlikely to win, it is sometimes said that they are "out of the race" - even though they may still be competing, because they have so little chance of winning that they might as well be out of it.

The inference of the entire quotation then is that Hilary Clinton's effort to become president was not looking hopeful, and that she was considered "out of the race" when an event happened that changed public opinion so much her chances began to look hopeful again and this moment effectively "put her back in the race".

Answer 2

Her is an object pronoun, not a possessive one, and back is an adverb.

It parses as "This was one of the moments that ... put her [back into the race]".