Sounds like an easy question, but the answer isn't so simple.
I figured I'd go to the National Climatic Data Center, and sure enough, I found a web page for "National Snowfall and Snow Depth Extremes." Ah, an answer.
But, years of wasting time reading about snow caused me to scratch my head about the numbers above. I seemed to recall that California had some prodigious snowfalls. Indeed, it's easy to find web sites with conflicting numbers from California. In particular, many claim that the monthly snowfall record is actually 390 inches at Tamarack, CA in
March January 1911 and the single storm snowfall record is 189" at Mount Shasta Ski Bowl from Feb 13–19 1959.
I'm not sure why the difference in the monthly snowfall record, especially since it appears the NCDC data above includes an analysis of March 1911. Perhaps the March 1911 data was deemed suspect? I also wonder if the Mount Shasta record might extend over slightly longer than 7 calendar days and thus doesn't meet the bar for a 7-day records.
Got any clues? Let me know.