Why Swap Spreads tend to negatively correlated with Treasury rates themselves???

One story sometimes heard about this is that the demand for yield pickup increases when Treasury rates are low. Higher demand implies a lower yield.

Could you expand on this a little more - I've found that swap spreads usually decline as treasury yield decline and vice versa

The correlation depends on the time frame.. In the late 90s spreads were negatively correlated with USTs. As Treasuries rallied, spreads widened to compensate, and all-in yields moved significantly less than Treasury ylds. (Consequently, swaption vol traded a lot lower than UST vol)Over the past 5-7 yrs, however, swaps have gone from being a credit instrument to the primary interest rate liquidity instrument. The was partially the result of reduced Treasury supply, and the resulting repo "problems," but also the result of a maturing swap market with a number of credit mitigating factors. Over the past 5-7 yrs, swap spreads have been positively correlated with Treasury yields. When mkt participant want to get long the mkt, they will buy USTs AND receive on swaps, compressing both.