Can we use will or shall in past tense?

[ravikumarkargam]

In yahoo news, I encountered the below statement.
President Bush predicted Monday that voters will replace him with a Republican president who will "keep up the fight" in Iraq.
Here, will is used in past tense statement. Is this right?
If yes, in what occasions can we use future tense words like will, shall as part of past tense.

I am expecting the statement should be
either
President Bush predicted Monday that voters would replace him with a Republican president who will "keep up the fight" in Iraq.
OR
President Bush predicted Monday that "voters will replace me with a Republican president who will "keep up the fight" in Iraq".

Please advice me.

Thanks,
Ravi

[Tdol]

If the verb is still in the future at the time of reporting, we often don't change the tense.