The White House yesterday dismissed the Senate Budget Committee's rejection of an administration-blessed budget blueprints as an "accounting problem" and a "bump on the road" and insisted that its economic program is still on track.

And in what could signal a break in the impasse, Sen. William L. Armstrong (R-Colo.), whose vote was critical Thursday in defeating the budget proposal, also said he has "no doubts" that a solution can be worked out by identifying enough future spending cuts to assure a balanced budget by 1984.

But Budget Committee Chairman Pete V. Domenici (R-N.M.) was less sanguine in talking with reporters as he groped for a way to reverse the 12-to-8 vote by which the committee Democrats, with the aid of Armstrong and two other Republicians, rejected a budget resolution for fiscal 1982 that was tailor-made for President Reagan's economic program.

Asked about comments by some of his Republican colleagues that the vote impedes chances for passage of the administration's three-year, across-the-board tax cut, Domenici said, "Sure I think it has." He also expressed doubts about resorting to what he called "false" and "hypothetical" budget cuts for future years that would give the appearance of budget balancing.

Domenici hinted that he may be forced to turn to the Democrats if he can't come to terms with Armstrong and his two allies, Sens. Charles E. Grassley (R-Iowa) and Steven D. Symms (r-Idaho). He declined to make any overt threats but stressed that he would get a budget out of committee "any way I can do it."

The Democrats are linked to the tax cut issue because they cited objections to Reagan's proposed tax cut as one of their principal reasons for voting against the budget. For the three Republicans, the main problem was deficits, prinicpally lack of sufficient identifiable cuts to guarantee the balanced budget in 1984 that Reagan has promised.

Although the vote was widely interpreted in Congress as a setback for Reagan's program, Armstrong, a strong Reagan backer, sought to downplay that interpretation, saying he voted against the budget proposal only because he thought a vote before the Easter recess was "premature." Added Armstrong: "We just hadn't finished the job."

White House officials, some of whom talked with Armstrong earlier in the day, picked no public quarrel with him.

"I think there's far less there than meets the eye," said Office of Management and Budget Director David A. Stockman in an interview with wire service reporters.

The problem is that the administration counts on balancing its budget in 1984 by means of budget cuts it has not yet submitted to Congress. These unspecified cuts turned up as a $44.7 billion deficit in the committee's projections for future years, raising the hackles of dedicated budget-balancers like Armstrong.

"Some of the Republican members want to include our future savings as unitemized, within the budget," said Stockman. "The chairman [Domenici] wants to include them as theoretical deficit, below the line. It's the inability to resolve that difference in accounting that caused the breakdown . . ," he added.

Armstrong said he agreed "in spirit" with the notion of an "accounting problem" but said he will insist on such things as strengthened presidential powers to rescind appropriations and congressional controls over spendout rates for federal programs, which he said could save about $25 billion a year. And $20 billion could be saved from program cuts already identified as options by the committee staff.

But Domenici indicated he was skeptical. "I really don't believe it is technically feasible or politically feasible to go through [the budget] and find out-year [future] target cuts . . . . It's just baloney."

Meanwhile, Stockman indicated support for a slightly revised administration budget outline that House Republicans, in cooperation with Rep. Phil Gramm (D-Rex.), are pushing as an alternative to the Democratic-drafted budget that was approved Thursday night by the House Budget Committee.

"Basically it's the administrations's program with a few wrinkles," he said, adding that he expects it will pick up enough votes from conservation Democrats to carry in the House when it takes up the budget after the Easter congressional recess.

House Democratic leaders are also angling for support of the same group of conservatives, who appear to hold the balance of power in the House, and are expected to bargain further with them after the recess, with trade-offs between defense and social spending being among the main chips.