This is completely dependent upon how big, how elaborate, and how sturdy this thing would be. Bear in mind, the character would most likely be hiring labor to do the actual work. I think that a character would most likely act as foreman, directing the manual (primarily unskilled) labor.
Well, you can always go by the fact that, since there are plenty of mansions in the world, that a low-level expert would be able to figure out how to build one. I'd say that 3rd level would be fair for an experienced Expert. Furthermore, we can assume that they're fairly bright (say, 12 Int or so), and have maxed their ranks in Knowledge (architecture and engineering) and Craft (carpentry). Furthermore, they've probably taken Skill Focus (Knowledge [architecture and engineering]), along with Skill Focus (Craft [carpentry]). So, we have a dedicated carpenter / construction worker here, with a +10 modifier to each skill. Odds are, to ensure a steady rate of success, they'd be taking 10 for the most part. I'd say that a DC 20 check for directing the labor would be sufficient, with a lower result impeding progress and a higher result expediting it.
As for how long it would take, perhaps price the total mansion, and use a combination of each worker's Profession or Craft checks GP result to determine progress, with the mansion being completed when the total price is met or exceeded. Each worker would probably gain a favorable circumstance bonus (+2 or so) for being guided by an Expert in the field, assuming he makes his DC 20 check. I'd say that they get a +2 bonus for the Expert making the two DC 20 checks (+1 each), with an extra +1 bonus for every time the Expert exceeds the DC 20 check by 5 (5 over = +3, 10 over = +4, etc.), and no bonus if they fail the check. So, if the Expert took a chance and didn't take 10, and rolled a total of 25 for each check, then the workers would each get a +4 bonus to their Craft/Profession checks, which would speed up progress considerably.
Complicated, yes, but base-building is a pretty intense thing to undertake.