Even as President Carter is said to be contemplating cuts in the budget he sent Congress last month, the Pentagon is saying it will need further increases.

Gen. David C. Jones, chairman of the Joint Chiefs of Staff, has told the House Budget Committee the military will need "substantial" increases in spending beyond those Carter has already proposed.

Jones did not say what amounts the Pentagon has in mind, and the White House may in the long run overrule the services.

But his testimony at a budget hearing Thursday illustrates the problem that Carter and Congress are likely to have if they try to cut the deficit to fight inflation.

Carter has proposed a deficit of $15.8 billion for fiscal 1981. Many experts think the real figure will turn out to be a good deal higher than that, not lower as the economizers would prefer.

First, they note that Carter's budget bravely presumes that Congress will vote about $5.6 billion in so-called legislative savings, even though Congress has rejected or deferred some of the most important of these proposals before.

"Moonbeams," Rep. Barber Conable (N.Y.), ranking Republican on House Ways and Means, called these presumed savings the other day.

Among them are a hospital cost-containment bill that would reduce Medicare and Medicaid outlays which Congress has now voted down twice; a new federal pay system that would cut costs; a cut in the school lunch program so that subsidies would go only to the poor and no longer to the middle class. This last was first proposed -- and rejected -- in the Johnson administration.

Second, the budget also presumes that Congress will approve a series of small tax increases, particularly a $4.5 billion one-time-only increase through a speedup in collections. But the tax committees in both houses have already indicated they are unlikely to approve this speedup.

If Congress doesn't vote the budget cuts and tax increases Carter has already proposed, the deficit would be close to $25 billion.

Then there are the economic assumptions on which his budget estimates are based: that inflation will fall somewhat and unemployment will rise as the economy moves into a mild recession. Inflation increases both government revenues and costs. Unemployment cuts into revenues while also increasing costs (of such items as unemployment compensation and food stamps, for example).

The Congressional Budget Office suggested in a report that the recession may be a little more serious than the White House has forecast. If its recession and other assumptions are correct, the CBO said, the deficit will be $5 billion to $10 billion over the White House projection.

On the other hand, inflation can help narrow the deficit. If oil prices rise more than the White House has forecast, and it seems likely they will, then revenues from the president's proposed tax on crude oil will also be higher by several billions.

Conable, in fact, is one who thinks the deficit could turn out smaller than anticipated, mainly because of inflation, which increases revenues faster than costs by lifting people into higher tax brackets.

Finally, there is the defense budget, roughly a fourth of the spending total. Carter proposed $146.2 billion in defense spending next fiscal year, an increase of roughly $16 billion or about 12 percent. Defense was one of the few parts of his budget to increase in "real" terms -- that is, more than inflation.

And now it turns out that even this increased defense budget underestimated some likely costs. The Pentagon assumed fuel prices next year would still be at last year's level. They are already higher; its fuel bill in fiscal 1981 will be $4.5 billion higher than estimated, one budget expert said.

The services and their supporters in Congress also point to recent events in Iran and Afghanistan as evidence of increased needs.

The administration is assuming for now that the Pentagon can be made to eat any increased costs, and that total defense spending next fiscal year can be held to the budgeted level.But, as a budget expert said this week, that requires "some heroic assumptions."

There is also this fiscal year's record to look to. Carter said in his budget a year ago that the deficit in fiscal 1980 would be about $25 billion. Now he is estimating it at about $40 billion, and the year still has seven months to go.