My thoughts are based strictly from the movies.
I believe that it is illogical to assume that
everybody loved and respected Eomer. To know that for certain one would have had to canvass the entire nation of Rohan, asking every person what they thought of Eomer. Therefore, it is logical to assume that there were certain people (Grima, for instance) who disliked Eomer and would have been extremely happy to have seen him punched and ill treated.
It is also logical to assume that Grima went around the troops finding those who could be easily swayed with lies (I do believe that the movie mentioned and showed to a small extent that Grima was a liar) or who already had a dislike for Eomer. Thus with poisoned words and lies, he could gradually build up his own little army around the king to deal with people like Eomer and Gandalf (remember, this is
purely from the movie perspective). Having his own little army would make sure that King Theoden "stayed in line" as it were and didn't become conscious of the lies, etc.
Those are my speculations on the subject. It seems to me that is what traitors do: they go aroud finding people to agree with them. Then through intrigue and whatnot they try to come to power etc. Grima is, in a word, a traitor thus it is logical that he would do that
from a movie perspective.
So no, Eomer. The soldiers were probably not mindless drones. They were probably just Grima's henchman -- as well as stuntman to provide the viewer with edge on their seats suspense! *cough*
As it is, of course, that's not what happened in the book. Grima poisoned the king, the soldiers disliked it but couldn't do anything about it, etc. etc. etc. But...this is a movie...not a book...