I think we have a winner!

I believe Diane is correct in her comment on my previous birdtastic post! I just googled House Finches and here's what Cornell's Ornithology Department page about them says:

"A bright red and brown-striped bird of the cities and suburbs, the House Finch comes readily to feeders. It also breeds in close association with people, and often chooses a hanging plant in which to put its nest."

Now, the pictures on the page aren't an exact match for the birds as I've observed them through the window, but certainly are close enough, as are the eggs. So, unless someone can definitively state otherwise, House Finches they are!

Thanks, Diane!