Actually it usually takes about 3 hours and 15 minutes for us to go through the narrows in our houseboat, however depending on the time of day it could cost you an entire day, especially if there is a lot of traffic. If you rent a houseboat it is very possible that all the campsites will be taken and you will have to keep steaming up the lake, often till dark. With the cut open you can easily find a camping spot in the daylight.
For more information you can check Waynes Words, his board is crazy about Powell and the CRC...
Waynes Words They say it is going up 4" an hour. So if you have a pontoon style houseboat you will most likely be able to make it through sometime tomorrow. If you have one of the newer v-hulls it might be Sunday before you can make it.