When people say that welfare should be cut, I always hope they don't find themselves in a desperate situation where they have to turn to others for help. I've worked with welfare recipients for years. Yes, there are some who abuse the system. There are people who abuse every system. However, those folks are in the minority but they do give a bad rap to the majority who are just trying to feed their family. Welfare recipients are people who have just had lousy luck or found themselves in temporary difficulties; sometimes they are students trying to get through school. Sometimes they are young adults who have been thrown out of the family home. There are lots of reasons people find themselves on welfare, and what they receive is not enough to make ends meet. It's always easy to target welfare recipients as a bunch of lazy bums who just want government handouts, but this is not at all the case for the vast majority.
Aside from those who are disabled which should be in a different program, there are two main groups of people who needs welfare.
The first group is as you said, young adults who are just starting out. While assistants may be necessary for this group, it should be in the form of loans rather than hand out. Young adults have great future earning potentials, so there's no reason to just give them the money. Banks also like to work with young adults since they could be future customers. The government can provide some form of loan guarantee for a fee, I don't see why the government should spend a lot of money on this group.
The second group is people who are older, but less prepared. The PBS has an article on 99ers, who are people who ran out EI after 99 weeks in the states. Pretty sad stories, but you can see they have nobody but themselves to blame. One guy worked for 22 years and earned near 6 figure salary, yet he lost his everything after only several months. There will always be tough patches in life, the trick is to be prepared for it. The left seems to think people can't be trusted with their own lives, the government has to think for them. I think the government should dispel the myth that society always has your back, then maybe people will be more responsible with their own lives.
There are certainly always exceptions, but they are not the majority.
Work hard, live well below your means, save at least 10% of before tax income, invest wisely, and one will find that when bad luck strikes, one is better prepared. I don't think welfare should just be cut, it should be reformed to target those who have been responsible and really just need a hand. The recipients should be expected to repay the system to make it self sustainable in the long run.