So Lee had been asking Jackson to start moving for weeks on end, with requests on the 14th, 18th (warning that Burnside was making for Fredericksburg), 21st and 23rd; Lee did not know Jackson had started moving on the 21st until after he sent that (23rd) request. This means that at latest the message which set Jackson moving was the one on the 18th, which is when Lee himself starts moving, so the timeline of the components of Lee's army moving (especially Jackson) is pretty much set.
The route that Jackson's force took historically was about 135 miles long and took 11 days. To reach the North Anna (specifically Doswell VA) is 148 miles and would thus take 12 days; Jackson would consequently begin to arrive around the 2nd of December.
From Fredericksburg itself to the same point is about 36 miles. If we assume that unopposed pontoon bridge construction takes one day (starting on the 17th when the head of the Union force arrives) and that the army as a whole will take another two days to cross, and that Burnside does not begin to move until the day after that, then the timeline is thus:
17th: head of Union column arrives, pontoon bridges built
18th: Lee begins moving from Culpeper towards the North Anna, orders recce to Fredericksburg
18th and 19th: Union army crosses Rappahannock
20th: Burnside starts moving south, he has 36 miles to move
21st: Jackson starts moving
If Burnside can manage to move at an average of four miles per day, he will still reach the North Anna area on the end of the 28th. He will then have three to four days before Jackson arrives.
I think there is no reasonable circumstances under which Lee can hold the line of the North Anna. It's in fact quite plausible that Burnside moving at a more realistic speed could use one Grand Division to cut Lee off from Jackson's arrival, use a second to hold Lee in play, and send the third around and cross downriver (in the way Grant did in 1864).