I think people have pretty much covered these basic points, but here's my overview:
Capitalism is effective because it assumes the "worst-case scenario", that people are completely and utterly selfish, and manages to work anyway. The problem is that keeping a human being alive, healthy, and reasonably happy takes a significant amount of effort. The hypothetical completely selfish people say "Why should we go to all that effort? Justify the expense of keeping you alive." As such, people have to work to stay alive. If they cannot work, bad things happen.
Welfare is an attempt to mitigate this issue, by providing the basic necessities "for free", but the effort has to come from somewhere. The people providing the effort (or who are made to provide the effort) can end up unhappy about providing services to people who aren't necessarily giving anything back; perhaps not quite as badly as the hypothetical completely selfish person, but the sentiment is there.
The ideal solution might be to simply provide the welfare anyway, and have the unhappy people simply DEAL WITH IT (insert your preferred memetic image here), but this is subject to the same problem as other "ideal solutions" like communism, namely that evolution has left humans fairly selfish, even if they aren't completely selfish. It's not a stable situation.