the protests hardly impressed

It means the reference to size of the demonstration, had no effect on those who wanted to enforce illegal immigration legislation.

The meaning is fairly clear from the sentence, taken as a whole:



In other words, certain people (i.e. those who favour stricter controls on illegal immigration) were not impressed by the protests.

Try This?
“I think it’s only fair that I speak up for those who can’t speak for themselves,” said Aimee Hernandez, 28, one of an estimated 400,000 people who turned out in Chicago, at the site of one of the largest demonstrations. “I think we’re just too many that you can’t just send us back. How are you going to ignore us?"
But among those who favor stricter controls on illegal immigration, the protests were hardly impressive.

He is speaking collectively; in your quote, the tenses are changed. The tenses must remain constant.