Ever since Maidan, ultra-nationalist organisations, which were before most active in Western-Ukraine, have gained quite a foothold in the capital Kyiv. Though I think they do not pose a threat to the government, they do represent a formidable part of the population. Also, some of these groups are nurturing the future nationalists of the country.
2017.02.22. Kyiv - The day of ousting Viktor Yanukovych, ex-president of Ukraine
It is hard to tell if they are patriots, nationalists, or hardcore right wing sympathizers. Probably you can not categorize these people, but I can say: they still can be mobilized.
I do get the impression, that most people are tired of protesting, and are worn down that things keep turning worse than before. Nevertheless, there are still plenty, who can be called upon to act. Do not forget, that during the times of Maidan, it was not the city if Kyiv, but thousands of protesters who managed to overthrow the government.
Just imagine: in a country of 45 million people, a few thousand people change politics.
That is something any government should fear of being repeated.