Criminals getting a raw deal is hard to sell to an electorate who actually work for a living. The best way to sell it is that non-criminals can reduce their tax burden.
I think the best way to get serious reform is to point out the relationship between crime and punishment has gotten a bit too loose, and that it's a matter of basic justice to expect the punishment to fit the crime.
"Those other guys aren't my problem" is a general consensus and "those other guys who got through our great court system and were found guilty" is a huge barrier to overcome for most people, even though it is a bogus sentiment for a ton of reasons.
And to be fair, a lot of research was showing that repeat offenders were a problem for society, it has been shown that the harshness of the prison system and the after effects are why, but if you don't know that link then saying "well they keep doing it so lets take care of the problem" while simultaneously discouraging repeat offense makes sense. Again underlying those things is falsehoods and three-strikes is a terrible idea, but it doesn't take much thought to see why it became so popular.