Yes, Jesus most definitely washes us - I probably did not word that well. Certainly, without even investigating the mechanism for that washing, it is clear that Christ's sacrifice deals with the believer's past guilt.

Digging deeper, ultimately, we have two sin problems - our past guilt, and our tendency to keep on sinning. Suppose that someone is convicted for stealing and goes to prison, but after five years, the authorities realize they imprisoned an innocent person. When they find the true perpetrator, the judge will not reduce his sentence according to the time the first man served, will he? This western notion of punishment is the same as found in the Bible. Ezekiel 18:4 says, "The soul who sins will die." Thus, Jesus can only justly pay for His own sins. Therefore, to pay for our sins, Jesus must make us part of Himself. Consequently, He gives us His life to dwell within us, His blood to flow in our veins, thus making us members of His body. (For fascinating prophecies of Christ taking on our sins to the degree they are considered His own, see Psalm 40:6-8, 12; Psalm 69:9, 5.) This union with Him enables Him to effectively deal with our first sin problem, which is our past guilt.

This union also enables Christ to deal with our second sin problem, which is our tendency to keep on sinning. If we are members of His body with Him as the head of that body, then He is in control of us. His blood, His life flowing in us, changes us from the inside out. He works in us to give us the desire and ability to do His will, even when we are not fully aware of His working (John 3:8; Mark 4:26-29).

This union with Him conveys the full sense for His blood washing us. He washes us by dealing with both of those sin problems.