We study the relationship between volatility and liquidity in the market for on-the-run Treasury securities using a novel framework for quantifying price impact. We show that at times of relatively low volatility, marginal trades that go with the flow of existing trades tend to have a smaller price impact than trades that go against the flow. However, this difference tends to diminish at times of high volatility, indicating that the perceived information content of going against the flow is less when volatility is high. We also show that market participants executing trades aggressively using market orders will experience larger increases in price impact than those executing trades passively using limit orders as volatility increases. And times of low market depth are associated with increased risk of high price impact and high sensitivity to volatility in future, perhaps because liquidity is more reliant on high-speed quote replenishment and is therefore more fragile.