I don't think the issue is one of a time-limit as much as someone being given money to do nothing....even if they are able. Jesus very clearly said, "he who will not work, should not eat". For those that are truly destitute, some assistance is needed. But NOWHERE in the bible does it say it is the State's responsibility to care for the poor. It is the responsibility of individual's like you and me to personally help those who can't help themselves.
People forget that in the US long before we had the Welfare State, there were private charities. (You should read about the history of charity in the US; it's quite interesting) Through the efforts of Churches, institutions and individuals, people were given shelter, clothing and food. But it wasn't "FREE". You had to help the organization/person if possible by cooking, cleaning, sewing, chopping wood, painting, etc. to earn your keep. In those days, any self-respecting person would consider it below their dignity to be given a handout. They would insist on doing something for the help they received.
Today, people expect the nameless, faceless entity called government to send them a check, food stamps or whatever else they need, without having to do anything. But we are the government, we pay the money that goes into somebody else's pocket. We worked for what someone else didn't. There is little to no gratitude involved much less responsibility. This type of system kills the work ethic and the person's soul. By nature, every human being realizes they must produce or contribute in some way to society. Even disabled people have dignity and deserve a chance to prove whatever abilities they have. No one should be robbed of this.
On a personal note (and I've shared this before) my sister and her husband have 7 kids. She had quads, twins and a singleton all in 3 years. That's a family of 9 people on one income. They have qualified for all sorts of gov. assistance including food stamps, WIC, basic health, etc. But they have refused all of it because they didn't think it was societies responsibility to care the children they created. So for many years now, my BIL has worked 2 jobs to support his family and still be a model father. I have many gripes with them, but I have always admired their hardwork and self-sufficiency. Naturally, the extended family mostly both grandparents and myself have done our part to help out. These kids don't have a lot, but they have never been deprived of the really important things.