The basic problem I have with the welfare state is not its goal, which is commendable, but rather its means of achieving that goal, which is theft.
The question that it seems we should be debating is whether it is okay in some cases to confiscate (i.e., steal) private property if you do something with it that most people agree is good.
I also have to think that there would be more private sector resources available to provide assistance to those in need if the government welfare apparatus was smaller.
A more basic question that always comes to mind is whether poverty, illness and other social misfortunes are the result of having too little government involvement in those facets of society, or whether there is a certain amount of poverty, illness and misfortune that just comes with having a population of 300 million or so people living within a nation's borders.
When you look at history it certainly does seem like rising standards of living are more correlated with societies that protect property rights, encourage productivity and have political institutions with somewhat limited powers than it does with societies in which government seeks to solve every possible social problem by redistributing society's wealth according to a bureaucratic plan.
I think that one of the core delusions of many statist politicians is that there will always a pool of surplus production that will be available for government confiscation and use in various world changing endeavors.
Of course any society that has upwards of 300 million people will have some poverty, illness and misfortune. The question is what is the best way to handle it.
There would quite probably be more resources
theoretically available to help the unfortunate if government didn't take so much in taxes but the question is would those resources actually be used to do so or not. IIRC the wealthier one got (and this was by income bracket...the studies were done by Indiana University and by a nonprofit group called Independent Sector) two things became apparent: one, the less as a percentage of one's discretionary income one gave to charity, and two, of what one DID give to charities/nonprofits, more of it went to arts and culture, one's own alma mater, supporting political causes and think tanks one agreed with, etc and less went to charities that provided basic human services (helping the sick, poor, homeless, etc).
One also has to consider that even if the rich and super-rich DID up their giving if their taxes went down do we truly want a quasi-welfare state run by the type of people who make up the top 1 and 0.1%? While the current welfare state is not ideal (and needs more of a complete overhaul than a a little tweaking IMO) do we really want people like Soros or the Kochs deciding (quite possibly based on their own political leanings) who should get help and who shouldn't?
I also think it makes no sense to say that even in the (hypothetical) complete absence of a welfare state (i.e. if TANF, food stamps, Medicare, Medicaid, SSI, and the like were all abolished but everything else stayed the same) that the government would not be redistributing wealth, income, and power vis-a-vis what would happen in a truly free market. You'd also have to abolish "welfare for the rich" (just for starters: corporate subsidies, bloated "defense" spending, the Carter doctrine and America's willingness to go to war to protect oil companies' interests, oil supplies, and sea lanes that that oil is shipped over, the prison-industrial complex and the War on Drugs, corporate limited liability and corporate personhood, the protection of titles to absentee land, patents and copyrights, laws that protect wlel-paid professionals from real free-market competition, below-market priced use rights to government-owned mineral rights/oil/gas, grazing land, irrigation, and timber land, non-enforcement or lax enforcement of pollution laws, eminent domain in the Kelo mold, "tort reform" that limits legal consequences for those rich and powerful corporations and persons who harm others, bankruptcy laws that let corporate bankrupts off somewhat easily (and let them dump their pension obligations on the government and by extension the taxpayers and don't even try to claw back things like "recapitalization dividends") but treat ordinary middle-class debtors quite harshly (thanks to the 2005 bankruptcy reform), laws that force businesses to act as garnishment agents on unsecured creditors' behalf, the Fed and its crony-capitalist below-market lending relationships with the TBTF banks, the FDIC, and bailouts in general) or else you wouldn't have a true free market but would instead have market discipline for working Americans but a generous safety net for the rich. To abolish our current "welfare state" without getting rid of or reducing the above would only serve to make the average American worse off in many cases by taking away what the government does to help him/her (even if such help sometimes does have unintended negative consequences) while at the same time leaving intact all the special privileges the wealthy and well-connected receive (and that generally make the poor and middle class worse off) from Uncle Sam and from the states.