As far as I know you can't do it in a day, as it's around 6 hours from CM to the border and regular transport from Huay Xai to Luang Nam Tha goes in the morning only.
I do remember a past post here though saying it is possible to do the trip in a day, so perhaps have a dig through the old posts and see what you can find.
I did it in reverse in a day. When the road was still bad, and with a break down. But that was headed the other way.
Seems like depending on demand, (and I'll bet it has increased now that word has gotten out that it's three and a half good road hours)they run two busses a day. Lao busses seldom run on schedule anyway. Most intend to leave around 8 or 9, and do if they are full. I'd bet it's similar with any second busses, intent on 11, if it's near full, they go. Lots of fairs waiting to flag them down on the side of the road.
It's easier headed for Chang Mai because they have all those empty mini vans that have brought folks up to take the cattle boat headed back to Chang Mai empty.
Look at it this way. Huay Xai has a lot to look at especially once the boat leaves in the morning things get nice. If you can't catch the bus, take a walk up to the wat on the hill. What's a day or two when you're on vacation. :-)
disclaimer - this info is from Dec 2006 (spent the night before in Chiang Khong & caught the first Huayxai-LNT bus next morning).
Changrai-Chiang Khong = 2.5h bus (hasn't changed, see http://laomeow.blogspot.com/search/label/chiang%20khong)
Huayxai-LNT: one bus around 9-ish that filled up by 8.30AM, second bus around 11.30ish but at 9AM was starting to be loaded with cargo. saw a report or two in late 2007 (after the road was completely paved) of a 'minivan' doing what seemed like an additional trip, not sure if it's something catering for tourists.
what time Lao buses actually leave can depend on what time the driver thinks it is, which may not necessarily be the same as what you think ;)
if you visit the wat on the hill that somsai mentioned (Wat Chom Khao), there are starfruit trees along the stairs leading up from the immigration, & part of the ceiling has paintings of the landmarks of Laos. back wall of the vihaan nicely decorated - most Lao temples leave that part blank. watched first sunrise of 2007 there :)