GOVERNORS and the White House began negotiating this week over whose government will be left holding what bag as the country moves forward through the 1980s. The White House opened the bidding with a modified version of its New Federalism Swap.

In the first round, the administration proposed a swap of programs--the states would take welfare and food stamps, the feds would take Medicaid. No one seemed to like that much, so the new strategy is to swap people. The feds would keep their responsibility for welfare and food stamps for the aged and severely disabled and take over medical aid for these groups. The states in return would take full responsibility for all help to families and the rest of the poor.

As in the earlier plan, the swap isn't as neat as it sounds. States would still be left paying the supplemental welfare benefits to the aged and disabled that most of them now pay as well as providing medical aid for other needy people in these groups who don't get federal welfare help.

To answer criticisms that some states would simply cut benefits for their wards, minimum guarantees are added. These protections don't amount to much after the first year. Unless states decided to be generous with their own money, even the very poorest welfare recipients could lose the inflation protection that food stamps now provide. And the working poor--many of whom now have total incomes far below the poverty level--would be allowed to lose one dollar in benefits for every dollar earned without exception so that, after payroll taxes and other work expenses were paid, they would be much worse off working than if they stayed home.

What is worrisome about the new proposals is not so much the details of the opening offer as the sense that the negotiations are proceeding at the level of a marble swap: "Here, you give me your grandmother and I'll give you one little kid and a worn-out worker--That's not enough?--OK, I'll throw in a quarter on the side--but don't ask me for more next week." Surely there are some larger questions that should be addressed before the bargaining begins.

What, for example, is the appropriate level of federal responsibility for national expenses other than those for social insurance, defense and interest on the debt? Under the Reagan budget plan, by 1987 such responsibility will all but have disappeared. Should the federal taxing power be used to equalize the large disparities that exist among areas in terms of burdens and tax resources? If so, what is a fair way to make the initial adjustment and how should it be changed as the fortunes of different areas vary? These aren't easy questions but they need to be resolved before the trading begins.