President Reagan's economic program ran into its first big bump on the congressional obstacle course yesterday as the Democratic majority on the House Budget Committee held ranks and rejected Reagan's budget-cutting blueprint in favor of a Democratic alternative.

But the Democrats remained uncertain as to their chances on the House floor -- so much so as to give them second thoughts about one part of their proposal, a "savings" of $4.3 billion from Reagan's generous spending proposals for the Pentagon.

Several Democrats said some of their proposed defense savings, possibily about $1 billion worth, may have to be revised or scrapped to prevent defections by conservative Democrats, who appear to hold the balance of power in the House on the budget issue. If Republicans, as expected, close ranks behind Reagan, the defection of 26 Democrats could down their party's counteroffensive.

House Speaker Thomas P. O'Neill Jr. (D-Mass.) also indicated that more money than the Democrats originally proposed may have to be allowed for defense. "If they [Pentagon officials] can spend more, we will increase that item," he told reporters.

In yesterday's vote in the Budget Committee, Reagan's plan was rejected -- and the Democratic alternative was given tentative approval -- by identical votes of 17 to 13, with the Democrats losing only their most conservative member, Rep. Phil Gramm of Texas, both times. The party-line split on the committee is 18 to 12 in favor of the Democrats.

However, the Conservative Democratic Forum, with 34 of its 44 members attending, met on the matter late yesterday and said it was "looking for other economies and a possible substitute" for the main Democratic initiative.

The Democratic alternative, unveiled Monday by Budget Committee Chairman James R. Jones (D-Okla.), uses savings from defense and other areas to restore more than $7 billion to social programs that Reagan proposed to cut, although Jones noted that it embraces about three-fourths of Reagan's recommended cuts.

The Democratic program claims to save $4.3 billion more than Reagan's. It provides for less of a tax cut than Reagan's plan and anticipates less of a deficit. It also contends that Reagan overestimates both the value of his savings and the likely performance of the economy over the next year.

Yesterday's vote did not lock the committee into any of Jones' specific proposals but means that the committee will be working within the framework of Jones' numbers rather than Reagan's in attempting to nail down initial spending targets for fiscal 1982. More importantly, it means that the House Democrats -- unlike their counterparts in the Republican-dominated Senate earlier this month -- didn't splinter apart in their first budget test.

As the House committee dug into the details of next year's budget, the Senate Budget Committee also began work on its first budget resolution for fiscal 1982. The two committees are approaching the same task in different ways. The Senate approved $36.9 billion worth of spending cut instructions to its legislative committees last week, leaving its budget targets until later. The House is working simultaneously on its budget targets and spending-cut instructions. Both houses are aiming to have this first phase of the budget retrenchment effort completed by summer.

As expected, the Senate committee, splitting 12 to 9 along party lines, went along with all of Reagan's economic assumptions for next year except interest rates. The Democratic minority contended that the administration was taking too optimistic a view toward inflation and unemployment as well as interest rates. The Republicans agreed only on interest rates, opting for a 12 percent interest rate forecast instead of the administration's 8.9 percent. The Democrats said it should be 13.7 percent. The House Budget Committee is also assuming a 12 percent rate.

The interest rate assumption is important because it affects spending projections and thus the deficit. The Senate committee staff estimates that the difference between 8.9 percent and 12 percent is $9 billion in extra spending by 1984.

Before the House committee got down to business, it somewhat painfully rejected two amendments aimed at balancing the budget this year. One, offered by Reps. Jim Mattox (D-Tex.) and Paul Simon (D-Ill.), would have eliminated Reagan's anticipated deficit of $45 billion (the Democrats say it's more like $50 billion) by foregoing most of his tax cut. It was defeated, 23 to 4. Another, from Gramm and Rep. Eugene Johnston (R-N.C.), would have cut spending to balance the budget. It was defeated, 23 to 5. The choice was so difficult for some Republicans that they simply refused to vote on either proposal.

Democrats twitted the Republicans who went along with Reagan's proposed deficit for what Mattox called a "radical departure" from their historic devotion to balanced budgets. Responded Rep. Jack Kemp (R-N.Y.): "We don't worship any longer at the shrine of a balanced budget."

Administration officials yesterday again attacked Jones' budget proposals as unrealistic and "not in the realm of compromise or bargaining."

Budget Director David A. Stockman said spending in fiscal 1982 must be held to below $700 billion. Jones estimates that the administration's own proposals would actually leave spending at $717.8 billion in that year, while his would cut the total to $713.5 billion.