The Republican-controlled Senate joined the Democratic-controlled House on the White House veto list yesterday as it prepared to take up a $15.6 billion supplemental appropriations bill for this year that includes about $1 billion in domestic spending the White House doesn't want.

The latest White House veto threat infuriated Senate Appropriations Committee Chairman Mark O. Hatfield (R-Ore.), who had attempted to accommodate several administration requests in drafting the bill.

It also reruffled some feathers in more conservative GOP quarters, according to Republican sources.

"What they're doing is testing how far they can go in running against Congress . . . , and that includes the Republican Senate," said one Republican senator.

"They're framing the campaign of 1984," said a leadership aide, speaking of both parties and of approaching tests of strength on tax and spending policies.

Today's congressional schedule illustrates how far the White House and Congress have progressed down the road toward a veto confrontation, at least over selected bills.

As the Senate considers the veto-threatened supplemental bill for this year, the House will take up a similarly threatened farm- and food-support money bill for next year. Meanwhile, House-Senate conferees will begin trying to iron out differences between their versions of next year's budget, both of which the president opposes.

Hatfield said that he had been informed by Office of Management and Budget Director David A. Stockman earlier in the day that Reagan advisers were recommending a veto of the supplemental bill.

Hatfield reportedly voiced strong objections and, according to other sources, was considering withdrawing his support for some administration-backed provisions, including weapons systems and financial aid for the International Monetary Fund.

Senate aides said that the White House objects to a variety of provisions, ranging from $370 million for construction of the Strategic Petroleum Reserve to $16 million for feeding the elderly to $12 million for research on AIDS (Acquired Immune Deficiency Syndrome), a newly discovered disease that the Centers for Disease Control has called the country's "No. 1" health problem.

They said Hatfield and others were particularly irritated by an implication that the White House will give Congress little, if any, discretion on domestic spending and will insist on its full military and foreign operations proposals.

They concede that the supplemental bill is about $650 million over Reagan's request but say that the administration, in asserting that it's too high by $1.1 billion, isn't counting cuts that the Appropriations Committee proposed.

Reagan's "veto strategy" emerged as it became clear that he will not get a budget of his liking from Congress. But until yesterday it appeared aimed primarily at the Democratic-controlled House. Now it is, as one Senate aide noted grimly, "truly bipartisan."

Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) joined Senate Majority Leader Howard H. Baker Jr. (R-Tenn.) in expressing support for a budget compromise while suggesting that there may be less than a "50-50 chance" of reaching agreement in the current climate.

O'Neill was especially strong in his appeal for a budget accord. "We the Democrats think it's a disaster for the nation if we don't have a budget," the speaker said. "If we don't set up a budget target out there, this is going to be government by confrontation."

In those circumstances, Reagan would "have a field day . . . . He's kind of aiming at it," said O'Neill.

Meanwhile, the House approved, 379 to 39, an appropriations bill for energy and water projects that avoided the usual controversy by excluding specified funds for such projects as the Clinch River breeder reactor and the Tennessee-Tombigbee waterway. No new water projects were funded, although funding may be provided later.

The bill also includes a 3 percent across-the-board cut in non-defense-related items, which is intended to shield the measure from a veto.