Hi,
It is idiomatically correct. It is better if you post the other options as well so that we can discuss why this is the best answer of the options. Moreover, we cannot simply change the original sentence unless and until it is really bad.

Hey frankenstein, even I felt kind of weird with "However much". Can you let me know some sources where I can have a list of idioms and phrases that appear on SC Thanks

Hey guys, My 2 cents:

However much United states voters may agree that there is waste in government and that the government as a whole spends beyond its means, it is difficult to find broad support for a movement toward a minimal state.

The part in blue is a Dependent clause and indicating contrast, while the part in green is Independent clause.

See, its almost same as we use Although X...., Y construction

Just like we never use BUT with Although because that gonna be redundant why?? because ALthough already indicates contrast or in simpler words includes a BUT in it...similarly However.... is dependent clause initiating contrast.

O.K. The problem I'm having here is that I don't understand the meaning of ''however much''. Does it mean something like ''it does not matter how much they agree''? It also sounds wierd

You can think of the "however much" as "no matter how much" or "to whatever extent" or "to however great an extent." It's similar to what you suggest ("it does not matter how much"), with maybe a tiny nuanced difference. That is that the phrase doesn't suggest a neutral "we don't care to what extent voters agree," but rather an "EVEN IF all U.S. voters agree that..., it is STILL difficult..." As atulmangal says, there's the sense of contrast in this construction.

Thanks Ashley!"no matter how much","to whatever extent ''- that's what I meant by ''it does not matter how much they agree''? Now everything's clear for me.

Ashley@VeritasPrep wrote:You can think of the "however much" as "no matter how much" or "to whatever extent" or "to however great an extent." It's similar to what you suggest ("it does not matter how much"), with maybe a tiny nuanced difference. That is that the phrase doesn't suggest a neutral "we don't care to what extent voters agree," but rather an "EVEN IF all U.S. voters agree that..., it is STILL difficult..." As atulmangal says, there's the sense of contrast in this construction.