won't vs wouldn't

[anhnha]

President Barack Obama said he won't have a discussion about increasing the nation's borrowing limit while Republicans hold a gun at the head of the American people.
More:Obama: Debt Ceiling about Congress Paying Its Bills - Politics - CBN News - Christian News 24-7 - CBN.com
Are both "won't" and "wouldn't" possible here?

 

[5jj]

Yes

 

[5jj]

Sorry, I do not understand why both of them are correct? Could you explain?

President Barack Obama said he won't/wouldn't have a discussion about increasing the nation's borrowing limit while Republicans hold/held a gun at the head of the American people.

When we report speech, we usually move the tenses back into the past (backshifting). That's why "wouldn't" is possible. If we do that, we need to backshift "hold" to "held".

If the situation reported still holds true at the moment of speaking, backshifting is not essential. That's why "won't" is possible.