The ends are secured, so how much load can a 6' span of SPF 2x4 support when turned on 3.5"?
Check out this site : http://www.msrlumber.org - it has all the answers to spans for most applications. There are several good sites that have tables, just google "lumber strengths".
The Sagulator says it will support about 375 pounds (evenly distributed) before there is noticeable deflection. I recommend you go to the site, read the notes, and play around with the numbers yourself.
The American Wood Council offers just the tool you need at http://www.awc.org/calculators/span/calc/timbercalcstyle.asp Maximum Span Calculator for Wood Joists & Rafters/ You'll want 'live load', meaning people (and/or stray deer).