Governors aim to modify 'new federalism',

America's governors have offered a counterproposal to the President's ''new federalism'' and Mr. Reagan considered it sympathetically.

Meeting with leaders of Congress and the executive departments this week, the governors proposed a more modest exchange of responsibilities than Mr. Reagan seeks, and the President expressed a willingness to modify his program.

Before adjourning the winter meeting of the National Governors' Association, the state chief executives approved by voice vote and without debate a rewritten resolution endorsing the proposed federal takeover of medicaid, but rejecting the counterbalancing proposal that states pick up welfare and food stamps costs.

Governors said they would rather accept other federal programs not specified. ''It's now or never,'' Senate majority leader Howard H. Baker Jr. (R) of Tennessee told them. However, Speaker Thomas P. O'Neill Jr. (D) of Massachusetts said Reagan's proposed swap may be a smokescreen for further budget cuts.

Statements by individual governors indicated concern about their own and the nation's economic problems and an abrupt drop in the stock market Feb. 22 emphasized the point.

The governors in an ''informal consensus'' said that state treasuries are heavily burdened and that they oppose transfer of federal control of food stamps and Aid to Families with Dependent Children to the states.

On the other hand, Gov. Richard A. Snelling (R) of Vermont, spokesman for the governors, said they were willing to have Washington assume the full costs of medicaid. According to a position paper the governors tentatively adopted, they would ''take over the responsibility for comparably costly programs. Governors are eager to be relieved of their part of the fast-growing medicaid program. Mr. Reagan proposes federalization of this program while states take over food stamps and AFDC programs.''

Meetings between governors and national figures here established a mood that is important in the governmental process. Noticeable was a nonpartisan approach within the governors' group which apparently has grown out of general worries about the recession.

Governors endorsed the concept of the new federalism but waited for more specifics. President Reagan's flexible response indicated continued discussion. A period of bargaining seems opening in which governors welcome federal assumption of the burden of medicaid and look cautiously at the responsibilities they are supposed to assume in exchange.

In a separate meeting at the White House with leaders of the National Association of Counties, Mr. Reagan said: ''We have no intention of dumping responsibilites on other levels of government without the resources to handle them.''

Meanwhile, as governors conferred, Wall Street hit an air pocket and the Dow Jones stock average dropped 13.04 points Monday to its lowest level since May 1980. The drop seemed to indicate uneasiness over the big US deficit and the uncertain economy.

Private and public comment revealed worries in the states over high interest rates, reduced housing starts, declining industrial production, and unemployment. Governors reached their ''informal consensus'' by a 36-to-5 vote, giving tentative support to the new federalism, the opponents all being Republicans who wanted stronger support.

''He really indicated he was willing to negotiate, to discuss any differences there are,'' said Democratic Gov. Scott M. Matheson of Utah, one of those calling on the White House.

Vermont Governor Snelling said, ''the proposal we put before him was an appropriate starting point'' for discussion.

The consensus said: ''The governors also believe that support for state and local governments should not be cut in the 1983 budget to the extent that state governments are weakened and left without the capacity to meet the new service delivery requirements of the President's plan for 1984 and beyond.''

Gov. John Y. Brown (D) of Kentucky told the President that takeover of AFDC would create a patchwork system, and Mr. Reagan replied that the present system has ''50 different levels of benefits.''

Governor Snelling left no doubt with Mr. Reagan that he and fellow governors would be fighting his 1983 budget cuts on Capitol Hill. Republican Gov. Lamar Alexander of Tennessee, a strong supporter of the new federalism, put it succinctly: There was not much ''budget talk,'' he said, because ''none of us expects the President's budget to pass.''

As the situation stands the President has made a proposal and the governors, a counterproposal; neither has closed the door. Mr. Reagan wants to offer a program to Congress next month and requires assurance of flexibility from the governors before going ahead.