A tough spending restraint plan proposed by the Senate Budget Committee survived its first tests yesterday as senators rejected last- ditch attempts to exempt veterans' benefits and school lunch sibsidies from cutbacks.

The proposals, defeated by votes of 49 to 39 and 69 to 18 respectively, would have forestalled cuts that budget leaders say are needed to maintain spending ceilings Congress approved last spring.

The Senate is expected to vote today on a provision ordering its Finance and Appropriations committees to cut $3.6 billion from already- enacted bills to make up various cost savings Congress promised but never approved.

The House also began debate on its own version of a budget resolution, but put off any votes until Wednesday. The two houses are expected to complete action on their budget measures this week.

Although the Senate tests yesterday both were relatively minor, the outcome bolstered Budget Committee leaders' hopes that the full $3.6 billion in cutbacks ultimately will be approved.

Finance Committee Chairman Russell B. Long (D-La.), whose support is vital to today's cutback effort, was absent for the school lunch vote but voted with Budget Committee leaders on veterans' spending.

However, sources say Long may try to weaken the cutback effort indirectly today by proposing a floor amendment that would give his own panel and the Appropriations Committee more leeway.

Long was not present last week when Senate Democratic leaders arrived at a compromise on the cutback issue, which had stalled debate on the budget resolution. Long had said earlier it would be impossible for his committee to make the requested cuts.

The cutback controversy is one of several that the two houses face this week. Another is whether to increase defense spending. A third involves whether to make room for a tax cut to counter the recession.

The Senate is considering a resolution that would provide for $543.1 billion in spending and a deficit of $28.4 billion -- $5.4 billion above the red ink figure that Congress approved last spring. The House resolution calls for a spending total of $548.7 billion and a deficit of $29.1 billion.

Neither measure provides for a tax cut and neither allows the full 3 percent rise in defense spending after inflation that President Carter has requested.

Budget Committee Chairman Edmund S. Muskie (D-Maine) warned yesterday that to increase spending and the deficit would only fuel inflation. Muskie blamed heavy lobbying by veterans and other groups for the two proposals put forward on the floor.

The veterans' benefit amendment, sponsored by Sen. Alan Cranston (D-Calif.) would have added $500 million to spending in that category, by reversing a Budget Committee order to cut $100 million and then by raising the spending ceiling $400 million more.

The school lunch proposal, introduced by Sen. George McGovern (D-S.D.), would have added $100 million. McGovern complained that cutting school lunch benefits would only hurt low-income youngsters.