Is a DSLR a must for consistently creating larger prints to hang on a wall and feel good about?
No. Recently there was an article at Luminous Landscapes where pros were asked to compare similar landscape photos (I think the prints were 12x18ish) from the new Canon G10 and a medium format digital Hasselblad, and guess which was which. Apparently it was pretty tough to decide. But a DSLR does have many potential advantages over a compact digital. Here are a couple that really stick out in my experience.
Pixel size has a lot to do with high ISO quality and dynamic range. A compact camera will perform best in bright light, and if dynamic range isn't too much of an issue in the scene, low ISO compact camera photos will compare well to DSLR photos. Once you get to ISO 400 and above though I think it's pretty easy to see the difference in large prints. Compact cameras start showing a lot of noise even in well exposed ISO 400 shots, while DSLRs (at least the Canon's I'm using) have almost no noise at ISO 400. Once you go higher than that compact digital camera image quality really tanks, while ISO 1600 from a DSLR often still looks better than ISO 400 on the compact camera.
The tiny format and super zoom lenses in most compacts make it difficult to get a shallow DOF. If you never use shallow DOF then no big deal, but I like having the option.
When deciding whether you feel good about a photo I say who cares what camera was used. Let your eyes and mind judge the finished photo. It's either good, bad, or mediocre, and being shot with a DSLR isn't going to save a bad or mediocre photo.
Another consideration is taste and style. We're all sort of taught that photographs are supposed to be sharp, and detailed, and an accurate representation of reality. Study up on the history of photography, and visit some art museums. You don't have to stay in that box; many, many photographers have ventured out of it in the last 150 years, and have created wonderful and famous photos. The key is to understand the strengths and weakness of your tools, and do your best to use them to your advantage.
On another note brought up in this conversation: there are pretty much contact prints and enlargements. If the photograph is larger than the actual film or sensor then it's an enlargement. Most wallet size prints are enlargements, unless they are medium format film contact prints (which would be a huge pain in the butt).