Could it be one of the cottony scale insects? A photograph would be most helpful.

I was wondering if one of the sawfly larvae, I've had those on both crabapple (pear slug) and rose (rose slug) - but I don't think I'd say fluffy when squished, more like wet yuck.

I've not been successful with posting photos in the past, I could try again.

Wet yuck sounds about right, but pictures of sawfly larvae aren't the right color. These are pure white, with yellow heads and are stuck quite tight to the branches.

I'll try to get a picture next one I see.

Got my answer. I had an arborist out to estimate a tree & shrub plan, and he knew immediately what I had -- cottony scale. He said there is a huge epidemic of them here.

No wonder the white icky part didn't move - it was an egg sack (capable of holding millions of eggs, it seems!) and the yellow head was the host scale. Disgusting.

Thanks, everyone.

Each egg sac may hold hundreds, not millions, of eggs.

It was the 'marshmallow fluff' clue that gave it away, lol.

"Each egg sac may hold hundreds, not millions, of eggs."

That's still hundreds too many for me! At any rate, it was the tree guy who said 'millions'.