THE WHITE HOUSE-Senate Republican budget package is not faring very well even in the Republican-controlled Senate. That's not surprising. You can't expect a difficult political compromise to hold up when its principal features are unbalanced and when its most powerful supporter, the president of the United States, seems lukewarm to some of its most controversial aspects.

It is true that in his address to the nation last week, President Reagan used his full rhetorical powers to enlist support for the budget plan worked out between Senate Republican leaders and administration officials. In describing that plan, moreover, he specifically described sacrifices to be asked from users of Amtrak trains, the Export-Import Bank and Small Business Administration loans. But when it came to cutting the purchasing power of Social Security and other pensions, a key feature of the plan, the president was less explicit.

Anyone unfamiliar with the details of Social Security law might have guessed that a bonus, rather than a cut, was in the offing. "We are asking," said the president, "the 46 million Americans who receive a retirement, veterans or Social Security check to accept a guaranteed 2 percent increase over the next three years, in place of the existing cost-of-living adjustment. If, however, inflation should rise above 4 percent, the amount above 4 percent would be added to the 2 percent." Did you follow that? No fair reading it twice.

Small wonder that Senate Majority leader Bob Dole, to persuade members of his party to cast a symbolic vote for the compromise package on Tuesday, had to promise them the opportunity to vote down the Social Security and other pension cuts later. Or that on Wednesday and Thursday the senators took that opportunity. Why should senators get out in front on so explosive an issue when later on they may turn around and find their president is no longer behind them?

Sen. Dole also ran into some trouble selling the defense part of the plan. Here again the president, last week, had been less than candid. While he talked about savings of $100 billion from the military, his plan called for Pentagon spending -- already about double its level of a few years ago -- to grow by another $23 billion, almost 10 percent. The Grassley-Hatfield amendment adopted yesterday by the Senate reduced the size of the increase somewhat and left the administration in a weaker position to deal with the House on the defense issue.

The Senate leadership will continue dutifully to take up the many amendments to the budget plan still to be considered. Because senators on both sides of the aisle understand that action against the deficit is important to the economy's health, there is still some chance that a reasonable package will finally emerge. The administration lost control when it refused to submit a realistic budget last February, and now it finds itself unable to regain that control.