Welfare, in the USA, needs to be drastically altered but I would never suggest that it be abolished. Currently it is broken and corrupt just like many American public social institutions but the solution isn't to just throw it away.
People who have not needed to live on any form of welfare are lucky and it is possible that those people could feel that they are unfairly paying for a service they don't need or utilize. It is easy to think that something is useless or a waste of resources if you don't need it but once you need it you will be wondering why it isn't more accessible or supported.
There are people who force themselves, out of terrible decisions they made, to be in a situation requiring welfare and it is frustrating having to support them but the majority of those who need welfare were forced to that point because of events out of their control. Little exists to help these people rise up. If you are in need of welfare you often are poor, in moderate or poor health and possibly in a sub par hygienic situation. These factors can make it difficult to get jobs or advance in jobs. People look down on you and politicians never really help because these people are seen as a drain on resources by those well off.
Welfare is to help those at the bottom rise up and currently it is failing those most in need. It needs to be made more efficient and less corrupt. It shouldn't focus on getting people off of welfare as soon as possible but on helping people increase their living standards to a sustainable and acceptable point. Only the most demoralized want to live on welfare for ever and usually they don't want to but the feel they are stuck. People have a natural desire to do something and to contribute to something; proper welfare gets them going and removes some obstacles that are oppressive and intimidating.