BOSTON--The Senate swiftly approved a $71 million bill yesterday to fund welfare checks and other emergency accounts that are running dry in the final weeks of fiscal year 1989.

In a vote that may set the stage for a battle with the House and the Dukakis administration over how much the cash-short state can afford, the Senate passed by voice vote the supplemental budget bill. The bill slashes $267 million from the House's $338 million version, which was already less than the figure proposed by Gov. Michael S. Dukakis.

Chief among the cuts was $192 million in Medicaid payments to hospitals and nursing homes.

"Literally, if we passed the Medicaid number in this, we would put ourselves into deficiency," said Senate Ways and Means Chair Patricia McGovern (D-Lawrence).

McGovern convinced the full Senate that the state, reeling from tax revenue shortages, did not have the cash to pay more than $71 million in bills.

The supplemental budget passed by the Senate is a stop-gap measure intended to pay some accounts, such as Aid to Families with Dependent Children and general relief, through mid-June with the other unfunded matters to be considered later.

There was no immediate reaction from the administration or House Ways and Means Chair Richard A. Voke (D-Chelsea), whose committee will have to make a recommendation to the House about what to do with the Senate's supplemental budget proposal.

The stripped-down supplemental budget offered by the Senate's Ways and Means committee was "limited to absolutely essential appropriations to cover payments to people who depend on state government," said Senate Minority Leader David A. Locke (R-Sherborn).

"There is nothing in that that really lends itself, in my view, to much opposition," Locke said in explaining the limited Senate debate.

With the administration already predicting a $250 million deficit this fiscal year, Locke said, "I think the more interesting question becomes, 'What happens next?' And I don't know that answer to that."