McCarthyism didn't have that much support from voters, so this isn't the issue, it didn't become law. The issue is that the elected representatives didn't do anything to stop it until it started having massive disapproval from voters.
Voters needing to massively disapprove of government abuse for the "checks and balances" to do their job means the democracy isn't working as it should, the government doesn't need to change the constitution they just need to keep disapproval low enough to continue with their illegal actions. In a true liberal democracy the checks and balances works, ministers who perform illegal acts are investigated and relieved of their duties without needing elected representatives to start that procedure.
I live in Sweden and I can't even find examples of a politician that blatantly ignores laws and procedures that get to stay for years here. I think the two party system is the biggest culprit, then you need support from both parties to remove criminal politicians, but that is very difficult to get when people have to vote against their own. In a multi party system each party is a minority, and allied parties are not friendly to each other, they gladly sink an ally to absorb their votes since the issue was the party and not the alliance, people wont move to the other block over such a thing.