Did you get that last part? He's got it right at first--the President "will propose" funding--but then loses it at the end. Congress appropriates funds. The President does not appropriate funds. Therefore, the Executive Branch cannot make available (not even in the passive voice) funds through a budget amendment or any other way. And Congress can choose to reauthorize ESEA when and how it wants to, education funding or not.
In K-12 education, the President will propose a $4 billion increase, including the previously announced $1.35 billion request to make Race to the Top a permanent program. Of that increase, $1 billion would be made available through a budget amendment when Congress completes an ESEA reauthorization consistent with the President’s plan.
Separation of powers, anyone?