AMERICANS strongly favor ''ending welfare as we know it.'' So do the president, Senate, and House. Even most welfare recipients say they don't think the current system works. Senate and House conferees are now sitting down to settle their differences on how far to go in changing the six-decade-old program. We believe the more gradual Senate version (overwhelmingly passed) will generally prevail, be signed by the president, and change the nation's course. Such widespread agreement over a general goal is rare. But is it right? Let's analyze: There can be little doubt that ''welfare as we know it,'' the president's phrase, does not work. No blanket statement is true of every individual case. But ''welfare dependency'' and children and grandchildren born into a welfare culture are far too prevalent. Welfare ''entitlement'' is not the root cause of teen pregnancy, broken families, inability to gain job skills, and school dropouts. But it is a major enabler of these terrible erosions of a healthy society. In short, welfare doesn't do what Franklin Roosevelt earnestly expected it to do: temporarily help people so they can get off welfare into productive jobs. Prof. David Ellwood, longtime researcher on welfare and recent adviser to the Clinton administration, says tersely that ''we've become quite good at doing the wrong thing.'' Federal welfare workers generally don't ask how they can help applicants find a job or solve family problems. They simply do a competent job of confirming eligibility and issuing checks. So will the 50 states do a better job? Alas, the answer is probably ''yes and no.'' There's logic in trying a new approach when the old has badly failed. The standard statement that some states have created innovative programs to help those on welfare find work is accurate. But block grants to states need to be carefully monitored. The chief danger is that over time some states might try to export their jobless by lowering benefits. But that's later. For now, there's sense in getting on with this experiment in helping America's lost under-segment back to work-fulfilled lives - and doing so along lines close to the Senate bill. One major virtue of that bill is its decision to fund child care. If the aim of the program is to help clients, primarily single mothers, discover how to work, the way to that goal is to provide temporary child care while young mothers go back to school, learn skills, get jobs, and hold them. To prevent backsliding by states charged with this new responsibility, the Senate bill also provides a contingency fund to take care of additions to welfare rolls during a future recession. A word should also be said here about the Earned Income Tax Credit, which was lauded by Ronald Reagan as a way of rewarding the poor who choose to work rather than depend on welfare. A tighter cutoff may be justified to prevent those with sizable pension income from qualifying for the credit. But the credit itself should remain so people who go off the dole to work are not penalized for doing so. Altogether, Americans can take satisfaction from the fact that three leaders who have at times been mistrusted - Bill Clinton, Bob Dole, and Newt Gingrich - have risen to the task of trying to fix what a majority of citizens know in their hearts has gone wrong. Get on with helping America's lost under-segment back to work-fulfilled lives.