Overhaul in what way? Make it more profitable for people that are on welfare, or make it so that it discourages people from remaining on welfare for any length of time? Tighten the restrictions on who is eligible and for how long, or make it so that more people can become eligible and benefits are extended indefinitely?
There are numerous ways the welfare system COULD be overhauled, but from a government perspective, their goal would likely be to eliminate the system altogether because it isn't profitable for the goverment to pay people to live in substandard housing, have numerous unwanted children, and refuse to look for work because the government is supporting them.
WHY won't they overhaul it? Because it would require an enormous expense for the government to do so.