I do believe that the U.S. Economy can recover without a housing recovery. Although the fall of the housing industry was a big part of the downturn in the economy, it is not necessary for the housing industry to recover in order for the U.S. To recover. A slow housing recovery would open up opportunities in the rental industry. It would also give citizens more flexible spending money to inject into other parts of the economy such as retail or automotive.
I do not think that the United States economy can fully recover without also having a housing recovery. Since the housing market caused a large chunk of the recession and was a gigantic bubble in financial terms, it is also needed in order to help the economy fully recover and get back on track.