What 'reform' Republican voters want is their GOP to recognize the reality of growing inequality that has eliminated the connection between economic growth and middle-class incomes, to shift its focus away from tax cuts for the rich, and to drop the fixation with the knee-jerk response of slashing every New Deal or Great Society program -- that help middle-class Americans. Well, there's a name for people with those views: they're called Democrats.
That's not at all a functional description of Democrats.
Maybe the more more pragmatic, rational, and conservative of Democrats want what you describe, but the lunatic fringe of the Democrat Party, the fringe that frequently finds itself in power, just wants to start there and keep on rolling.
They don't want to "recognize" a disconnect between folks bringing lower-class skills to the marketplace and then finding that they aren't able to command middle-class incomes. They want to legislate middle-class incomes for people who don't have middle-class skills. They seem largely oblivious to the fact that our economy has evolved enormously over the past 50 years, both in terms of technological innovations taking the place of factory-floor labor and in terms of the global economy flattening and Democrat-led free market agreements resulting in greater, global, competition for no-skill and low-skill manufacturing jobs.
For the most part they also seem painfully unaware of the difference between generational wealth, hedge fund billionaires, and a guy busting his ass spending $200,000 and seven or eight years of his life to get a good (modern and largely necessary) education, in order to earn a solid middle-class or upper-middle-class living. Their tax proposals lump the corporate cog and the small business owner raking in $250,000 a year in the same boat with the guy whose family has had a billion plus invested dollars dating back to the time of the Industrial Revolution and can live like a king off of capital gains alone.
They aren't just interested in preserving New Deal social safety net programs, they're interested in pushing entirely new programs (like socialized medicine) on an entirely new generation of Americans.
Since you stopped there I'll stop there but I'm sure we can both keep going.
You can continue pretending that all the Democrats want is for things to stay largely the same in an ever changing world (which paradoxically would make them "conservative).
And I can continue demonstrating that they're really quasi-socialist progressives who have no real interest in the middle-class backbone of this nation but rather pander to the lowest-skilled and lowest-income Americans in an effort to trade redistributed tax dollars for votes.
What "reform" Republicans want (and I can really only speak for myself here) are leaders who don't really care what grown adults do in their bedrooms, who don't turn their evangelical Christianity in to the cornerstone of their political platform, who aren't interested in legislating morality or waging war as a metaphor on every real or potential vice, and who aren't such bellicose chickenhawk idiots. But we want them to be just as conservative as ever, if not even more conservative, when it comes to the government spending money (that they don't earn, but rather take from people who work hard for it).