President Reagan came up $1 billion short yesterday in the first test of his new budget-cutting proposals in the Republican Senate.

In approving 87 to 8 a $7.6 billion appropriations bill for the Interior Department and related agencies this year, the Senate refused to make more than minor cuts; it would have had to cut $1 billion to stay within the new spending limits Reagan proposed last month.

Senate Budget Committee Chairman Pete V. Domenici (R-N.M.) said the bill roughly approximates total spending goals proposed by Reagan last March, before spiraling deficit projections prompted the president to seek further spending cuts this fall.

Reagan's second round of budget proposals met with quick opposition even among Republicans when he announced them last month. Republicans since have been groping unsuccessfully for some way to deal with them.

They finally decided just to forge ahead with the waiting appropriations bills; yesterday's was the first out of the box.

Reagan has vowed to veto bills that "bust the budget," but White House officials declined yesterday to say whether the Interior bill fits that description.

The Senate approved cuts totaling about $160 million, proposed by Sen. James A. McClure (R-Idaho), chairman of the Appropriations subcommittee on Interior, but, voting 61 to 35, rejected a proposal by Sen. Mack Mattingly (R-Ga.) to cut about $380 million more.

It also rejected, 57 to 40, a proposal by Sen. William Proxmire (D-Wis.) to cut $135 million in projected spending for synthetic fuels development. Amendments to increase spending for weatherization and other programs were turned aside as well--and by a vote of 48 to 43, the Senate refused to increase spending by $13 million, as proposed by Sen. Patrick J. Leahy (D-Vt.), to beef up investigation of an estimated $8.6 billion in oil price control violations by oil companies.

Even Mattingly's proposal, amounting to a 5 percent cut on top of what the Senate had already voted, fell substantially short of Reagan's request last month that spending be cut 12 percent across the board below his own March budget proposals.

McClure opposed Mattingly's amendment "reluctantly," noting that the Appropriations Committee had not been able to agree on further cuts and asserting that Mattingly's proposed cuts would have "almost no effect" on the impending deficit or on the campaign to bring down interest rates by cutting federal spending.

Sen. J. Bennett Johnston (D-La.) got closer to the political heart of the matter, pointing out various backhome projects, including several in Mattingly's Georgia, that might be jeopardized by Mattingly's amendment.

The House previously approved an Interior Department appropriations bill that differs in the aggregate only in that it counts $3.4 billion for the Strategic Petroleum Reserve as part of the budget, while the Senate version does not do so. The bills differ substantially in detail, however, necessitating a House-Senate conference before the legislation can be sent to the White House.

Action on the Interior bill came as the Appropriations Committee approved $10.4 billion for the Department of Transportation, also exceeding Reagan's September goal by $637 million, although it met the original target set in his March budget.

Meanwhile, the parade of ever-rising deficit projections continued-- but Office of Management and Budget Director David A. Stockman insisted that the administration is not "making a fetish" out of a balanced budget by 1984, observing that high interest rates and continued spending pressures may make balance impossible.

"The fiscal balance objective as symbolized by closing the deficit to zero by 1984 is now seriously behind schedule for a hundred little reasons and no one's particular fault," Stockman said Monday night. Rather, the objective is to bring "the revenue path and the spending path under an expanding economy into balance out there in the 1984 range," he added.