Seriously if you’re that worried try calling a few contractors ahead of time. Ask if you get in a bind if they’ll come help.

Also if you think there’s actually a good change it’ll happen grab a tarp, some 16’ pieces of strapping and a couple ladders and a roof hook. You can cut the tree enough to get the tarp on and toss down trapping vertically on top of the tape with screws fairly easily from a roof ladder. It’ll suck to do alone and won’t last forever but it’ll get the house 99% water tight quick.

It’s the water damage that’ll really cause the extensive damage.

Edit: buy it all at Home Depot and if you don’t use it you can return it Monday.