At the risk of a woefully one-dimensional and repetitive assessment, bonds are following stocks, and that's about all there is to it.  Oil can definitely factor into the equation, but on the instances where stocks aren't following oil, bonds have tended to hang closer to stocks (in terms of bond yield moving in the same direction as stock prices).

The overnight session began with heavy selling in Asian equities markets which immediately translated to selling in US equities futures and strength in the safe-haven bond markets.  10yr yields had fallen to 1.951 by 4:20am.  Incidentally, that's the the same time that a laundry list of almost any equity index bottomed out, along with oil prices.

Trading has been mostly sideways since then with the only hiccup being the 8:20am CME open.  The traders that begin their day at 8:20am were lined up to sell, but only until yields hit 2.0.  From there, bonds have reconnected with equities and oil for another push toward the lows.  10's are currently 7.5bps lower at 1.98 and Fannie 3.0s are 12 ticks higher at 101-15. 

(Notice that my focus there was on the 8:20am  CME open and not the 8:30am economic data.  That's because the 8:30am economic data was a non-event.  Bonds were totally sideways for a full 15 minutes following the data, but had moved quite a bit from 8:20 to 8:30am).

As far as risks are concerned for the rest of the day, we have to keep an eye out for stocks bouncing in line with overnight lows.  Transposing futures prices to NYSE, that would be an S&P price right around 1840.  The longer the S&P avoids dipping under 1840, the more pressure bonds will likely feel to shed some of today's existing gains.