Didn't expect that she did have a greenhouse, Ken. Winter growing in my latitude doesn't provide the optimal conditions that many annuals need but New Guineas tolerate it well, and that means even though most people think of them as bedding plants only, they can be pretty successful grown as houseplants, certainly easier than the garden variety-busy Lizzie. You direct her to the houseplant forum saying you might be wrong, but have an issue when I comment on them, even though I've grown thousands of them over several decades? ;-) You are correct in saying not to get too attached to it, because they're not expensive, and to keep them beautiful inside requires a learning curve. I'd say worth a try. You don't need high humidity, just don't put them in a furnace draft where they'll get heater scrub. They'll protest if they're underwatered, and they'll protest if they're overwatered, and if the light level isn't high enough, you won't get bloom. But no more difficult than some other persnickety houseplants. This post was edited by calliope on Fri, Sep 12, 14 at 2:33

I'd say more likely to be a species of Consolida (larkspur) rather than delphinium. Consolida ambigua (C. ajacis) has naturalized widely across much of the midwest so that it appears to be almost a wildflower :-) Self-seeds freely, which IME, delphiniums do not.

If those are its leaves below I'd go with Erodium. Given your location try E texanum.

Phlox bifida ? https://www.wildflower.org/gallery/result.php?id_image=32342