Potential Federal Reserve Twist

Please comment on this train of thought:  Under the Twist program being considered, the Federal Reserve would sell some of its inventory of short term (0-5 years) treasury bonds and use the proceeds to buy longer term treasury bonds like 30 year ones.  The sale of short term bonds would reduce the price of the bonds and raise their yields.  Would this raising of the short term treasury bonds yields have any impact on the interest rates offered by banks on their 0-5 year CD's?