The major justification for cutting unemployment and welfare programs in the 1990's and 2000's was to get John Q. Taxpayer out from under the collective dead weight of Reagan's welfare queens.
As we're discovering now, however, if you're intent on cutting these people out, there's really only one way to do it: cap unemployment benefits, either in terms of money or time (i.e., you only get $X worth of benefits per year or you can only draw money for X weeks every year). The problem with capping benefits, as perfectly depicted in this NYT piece, is that you throw out the baby with the bathwater. When the economy goes in the toilet (as it does every 10 to 20 years at least) the groups who are the first to lose their jobs and the last to find new ones rely on the long-term unemployment benefits that get the axe from the Reaganites. These people, however, are overwhelmingly from very groups that welfare was designed to protect in the first place: the poor, the unskilled, the old, and the sick, rather than some mythical group of lazy, yet eminently hireable able-bodied adults.
Put another way, the goal of welfare programs is to prevent homelessness and destitution. At any point in time when the economy is running short of full employment, however, benefit caps mean welfare cannot protect those in the most need of it. The choice, then, is between abiding some hireable people living off government largess on the one hand, and letting old and sick people become homeless on the other.