Tim Kaine actually said...

There would be some potential effect on ongoing operations, in the absence of an AUMF, that you would--

So, there would not be a worry about the absence of an AUMF affecting DOD's CT operations.

the AUMF provides broad authority to use force against al-Qaeda, the Taliban

the prospect of repealing the AUMF is precisely what the President has functionally asked us to do