This plant is Bowlesia incana, common name hoary bowlesia. According to wikipedia it is a member of the parsley family and a native to South America and the southeastern and southwestern United States.
According to debndal at The Garden Forums it does NOT have any spines or burrs and lasts two winters long. She didn't notice any flowers on hers, but wikipedia says it grows yellow-green flowers appear in the leaf axils, and the tiny inflated fruit is only 2 millimeters wide. (Which explains why you might not notice any).
Now, you know I had offered a giveaway to the first person who correctly identified this. Weel, I had asked about this and a number of other plants both here and on The Garden Forum and THOUGHT no one had been able to identify it yet (thus, the giveaway). Well, I was wrong. Somehow I actually missed the VERY FIRST POST on The Garden Forum in which pkponder identified this plant!
So, here's what I'm doing...I'm going to give away free seeds or a postcard to everyone who posted here. Since I only have one Carl's Jr. Coupon and don't want to waste it, I selected a few people who gave the most helpful answers and am giving it to the first one of them who claims it.
Linking up, among other places, at Garden Club Linky