Do you seriously think those actually on Maidan could have stayed there so long had they not had the support of the majority?
You are hopelessly romantic if you really hold this view. How long protesters can stay on a public square is not determined by whether or not they have the support of the majority, but on the infrastructure and funding available. Running an unsanctioned protest is busy work.
Starting from the basics: (1) portable toilets (2) field kitchens (3) shelter from weather (4) copious amounts of alcohol and tobacco (5) entertainment.
Whether it's Kyrgyz politicians tussling with each other for the White House, or Georgians sorting out their local beefs, or university students running an Occupy Wall Street protest - everyone has learned these basics. These things require money. Money is politics. I once read in an article that the protests in Kyrgyzstan cost the organizers a million dollars a day to maintain. That's just the costs of busing people in from the regions, feeding them with buckwheat porridge and vodka, paying some local pop star to keep them entertained, and paying a bunch of Facebook and Twitter influencers to shape the message.
That's not a lot of money, but it's still money. You can't sit on a public square for months on pure enthusiasm, regardless of how many care packages you get from volunteers. You need organization (beyond the logistics - you need organizational cells, and motivated cell leaders that will monitor morale and keep people engaged), and you need funds. As a reward however - you have a picture that can be used on national television, and that's more important than any "majority" of the population.
In the case of the ousting of Yanukovych, on the other end of the barricade you had all the usual suspects. His former underlings, his former minister colleagues, his old patrons. The only thing absent was new people. It was the same Tymoshenko, Yatsenyuk. Poroshenko, Tigipko, Tyagnibok, Lyashko crowd that's been there since 1991. They just co-opted the people's anger for their own political ends, and then kept it on a boil until the desired effect was achieved. Same as during the Orange Revolution. They had clear reason to benefit from throwing the support of their parties and their businesses behind the Maidan - and they did. They all did. Either monetarily or through being rewarded with powerful positions. The Maidan activists themselves got zilch.