I plucked off and crushed all the little critters I could spot, but they seemed to come back within hours. Dan positioned the finch feeder next to the rosebush, so that can't hurt. And in looking online for some natural solutions, I ran across this item about sticky traps.
Instead using yellow posterboard (really, who has that in the house?) I stitched some yellow fabric to a couple of narrow strips of stiff interfacing (OK, I do have that in the house) and added hanging loops of the yellow rick rack which also happened to be handy.
Then I just slathered them with Vaseline and hung them right on the rose bush.
To be honest, the thing looks pretty ridiculous with these yellow dangly things on it. Reminds me of old stories about medieval children with a poultices around their necks to ward off the plague.
But I'll be darned -- the traps actually seem to be working. I haven't seen a single little critter feasting on New Dawn's buds or leaves since I put them on yesterday morning!