I do not want to sound flippant, but that argument sounds pretty much like "In order to fly to the moon, we need a rocket and a bunch of dedicated, hard working people" We do have a bunch of dedicated and hard working people, so let's fly to the moon."
You seem to forget that mass demonstrations and mobilizations of the past were an outcome of the objective conditions that made it possible to sabotage the capitalist project - not the cause of it. That mobilization could prompt people to action but did not give them the weapons - they already had them. The mobilization simply asks them to use these weapons on a particular target.
The mutiny on the Battleship Potemkin (subject the famous film) is a case in point. The sailors were already in control of the ship's guns, the agitators merely persuaded them to disobey the officers and turn those turrets the other way. Or take the fascist coup of 1926 in Poland, which started as an empty show of force by a populist military leader Jospeh Pilsudski. Pilsudski had only a handful of units loyal to him when he entered the nation's capital. Most of the military were loyal to the government. However, the army was immobilized by a railroad strike organized by Socialists who saw Pisludski as "their" man (he used to be one, to be sure). Without the railroad strike, the coup would have been squashed like a bug. Later on, Pilsudski "paid back" his socialist supporters by imprisoning them, but that is another story. An important part is that what started as any empty show of force ended up grabbing real power solely because it persuaded people who already controlled the railroads to derail the military trains.
It is quite obvious that in today's organization of economy and society, the working class is far too fragmented and scattered across the globe to be able to derail the capitalist locomotive - with or without mobilization. So saying we need millions to go with us is like saying that we need a rocket to fly to the moon. Or assuming a can opener like in that old economist joke.
Wojtek