First, as some other folks have said, give them a weekly list, not every day, or every time one's announced.
Actually, that might burn them out... or, they might decide to batch them on their own, and think they'll get to it eventually.
Here's one: give them a weekly list, AND INSIST on a weekly meeting to discuss it. EVERY WEEK, without fail, without cancellations. Tell them that you'll also want a spot meeting, when you get critical updates (like yesterday's Java from Oracle, with it's 4 that had a CVA rating of 10 on a scale of 10). Insist that if you get those, they need to meet that day, or the next, or give you the pre-approval to put those in without consulting them.
The weekly meetings will get to them in relatively short order, they being so busy and all....
Also, here's another pushback: do you have a testing group, that runs regression tests before regular updates, and especially on ermergency ones? If no, question the committee how they expect you to regression test everything. Also, do you have test, as opposed to development systems? If not, that's another budget item the board needs to approve..
Make them do that real job, professionally. See how much they hate doing it, and maybe it'll go away.