"Supply" has several connotations/sources in the bond market.  Most pressingly, Treasuries are constantly thinking about their most direct form of supply--new Treasury issuance--these days as that issuance will be required to pay for fiscal measures.  So when a report comes out saying the Treasury Department is preparing to ask congress for another $200bln in SBA loans (as it just did), that means another $200bln of supply in the Treasury market.

Supply/Demand 101: higher supply = lower prices, all other things remaining equal.  And when it comes to bonds, lower prices = higher rates.

Supply considerations don't end there.  We also have extremely elevated levels of corporate bond issuance.  This can spur additional Treasury selling pressure for complicated and boring reasons (explained in this primer, if you're interested).  That's definitely a factor today.

Finally, there's a Treasury auction coming up at 1pm, and it's not uncommon to see bond traders shy away from buying in advance of auctions because the biggest players are forced to submit bids at auction.  In other words, higher yields and lower prices are viewed as a good thing for those traders who are forced to buy.

The net effect is a move to the weakest levels of the day in Treasuries (10yr up 10bps at .78%).  MBS continue to outperform, but are off their previous highs.  2.5 coupons are down only an eighth of a point on the day, but had been in just-barely-positive territory half an hour ago.  This doesn't create any meaningful reprice risk in this market, but reprices are a constant possibility for lenders with competitive rate sheet offerings.