(edited to remove land; I misread the Demo screen article)
The answer is: around 108 thousand soldiers. Soldiers are the game's unit of power; see
The inner workings of the Demo screen explained.
I looked at the code (I think it's CvTeamAI::AI_surrenderTrade()), and I had a sample game where I could delete one Warrior at a time until Monty changed from being willing to vassalize to not. The code appears to say Monty will decline to vassalize to you if:
* he doesn't like you
-3 Close Borders was not enough to make him refuse, but even if you have more than -3, you can give him Meditation or whatever if you have Alphabet. But when he offered and I said no, I became his worst enemy, and then he refused for that reason.
* his power is greater than the world average
It shouldn't be.
* his power is greater than 2/3 of yours
This is the key factor. I suppose Monty's power could vary if any barb units flip to him, but in my sample game, the minimum was 108K soldiers. Here's the breakdown of my power in that game, in K soldiers:
12 population (total city pop 24)
13 buildings (1 Wall x 2, 3 Barracks x 3, 1 Forge x 2)
26 units (6 Longbow x 3, 3 Warrior x 1, 1 Galley x 2, 1 Trireme x 3)
57 tech ( [Sailing, Hunting, Mining x 1] - [Wheel, Alpha, MC, Compass x 4] - [Math, Archery x 6] - [BW, Machinery x 8] - [IW x 10] )
By the way, some leaders other than Monty have a personality factor (iVassalPowerModifier in the XML) for how they judge their own power for this purpose.