But Mr. Clinton defined himself in 1992 as a New Democrat with such signature stands as his pledge to "end welfare as we know it." And whether the most stalwart Democrats approve of his stands or not, Mr. Clinton, looking toward 1996, has clearly adopted a two-track strategy of co-opting or defusing traditional Republican campaign issues, like welfare, while keeping his Democratic definition by highlighting such stands as his threat Friday to veto the Republican plan to save money on Medicare.

Mr. Clinton stopped short of calling the Senate bill a measure he could sign, and his aides said they would still like to see some improvements. But Mr. Clinton made his approval seem implicit when he said, "We'll be working hard to build on the bipartisan progress we've made this week."

The President has been looking for areas of agreement with the Republican Congress. "If we can find common ground on the issue of welfare reform," he said today, "surely we can find it in our efforts to solve our other problems." He added, "Let's do welfare reform, then let's do the budget and do it right."

The Republican response to Mr. Clinton's radio address was delivered by Bob Dole, the Senate majority leader and the leading contender for the Republican Presidential nomination, and House Speaker Newt Gingrich. "Once the Senate passes our plan this coming Tuesday," Senator Dole said, "We will get together and we'll resolve the few differences there are, and I hope President Clinton will sign the bill."

The Speaker listed his party's goals for the next 60 days as "balancing the budget, cutting taxes, replacing our failed welfare system with one that works, protecting, preserving and strengthening Medicare."

Despite the optimism of the Republican leaders, a battle over welfare still looms as the House and Senate seek to reconcile their bills. Conservatives have vowed to restore the measures rejected by the Senate and opposed by President Clinton because they say they are necessary to reduce births outside marriage.

After Republicans won control of Congress last November, Mr. Clinton's aides say, he began reassessing the mood of the country and became determined to return to the centrist themes on which he ran successfully in 1992. In the spring and early summer, he started staking out ground where Republicans traditionally have a campaign edge.