Washington — Democrats may have won at the polls last fall. But this week will tell what that victory really means as the House of Representatives votes on a budget that President Reagan calls ''a dagger aimed straight at the heart of America's rebuilding program.''
After two years of watching the President and Republicans roll over them, House Democrats picked up 26 seats and new self-confidence during the midterm elections in 1982. The Democratic leadership appeared to regain its authority over the lower legislative body.
But the Democratic strength has not been tried yet. The major legislative items this year, a jobs bill and social security reform, have been worked out with Republican cooperation.
The first real trial comes as the House takes up this week a Democratic-crafted budget that is the target of a verbal barrage from Mr. Reagan. He has gone to the airwaves twice in the past three days to attack ''the so-called liberal Democratic budget,'' even going so far as to suggest that the Kremlin will be smiling on the attempt to slow down modernization of the US armed forces.
''It's an important test of our House leadership,'' says a Democratic leadership aide of the budget vote, expected on Wednesday. Noting that there is more support and less grumbling among Democrats than in past years over budgets, the aide voices optimism that they will win this budget battle.
However, Reagan's persuasiveness is a wild card, concedes the House aide, adding, ''It's going to be a tough fight, especially when the President is raising the ante like this.''
Titled ''A Democratic Plan for Economic Recovery,'' the highly partisan budget passed last week by the House Budget Committee begins by announcing, ''The supply-side economic scenario promoted and implemented by this administration has failed.'' Its spending and revenue proposals would attempt to undo two years of Reaganomics.
The House plan calls for billions more in domestic spending, about $30 billion more in taxes, and a slower rate of growth for the military than the President has requested for fiscal 1984.
Soon after the House Budget Committee acted, President Reagan met with GOP House leaders. ''He told us he was ready to go work'' to defeat the budget, says Rep. Tom Loeffler of Texas, who was present at the White House meeting. ''He asked us to go all out.''
Business leaders such as the US Chamber of Commerce have already joined the fray by opposing the Democratic proposal.
In defending the Democratic version of the budget, the House leadership argues that the overall thrust of the proposal is correct, even if some of the details will be changed. Among the most controversial is a proposal for $30 billion more in revenues, which Democrats all but concede would not be enacted fully.
Such changes can be made in a conference with the Republican Senate, goes the argument.
''This is going to be a long process,'' said House Budget Chairman James R. Jones (D) of Oklahoma, last week. ''Obviously in conference there'll be some changes made.''
Mr. Jones made a plea for using the Democratic version as a ''starting point'' so that Congress can pass a budget to avoid ''fiscal anarchy.'' He defended the proposed 4 percent real growth in military as close to the figure favored by Republicans in the Senate. Moreover, he said that the House GOP is avoiding drawing up a budget alternative because they would have to cut domestic spending to show a smaller federal deficit.
Representative Loeffler says the GOP strategy will be to vote ''no'' on the budget this week, force it back into committee, and ''replace it with something that's a budget resolution, not a political document.''
Loeffler, who for two years has helped form a coalition of Republicans and conservative ''boll weevil'' Democrats, admits that he's facing an uphill battle this time. ''The numbers are not what they were,'' he says.
''It still remains to be seen how many Democrats are going to defect,'' says a House Republican leadership aide, who late last week said it was ''too early to say whether we'll pull out the stops'' to oppose the budget.
House Democrats are also cautious. They will need support from 218 of their 268 members, an 82 percent backing almost unprecedented for a budget resolution. But if the Democrats hold the line, the House leadership would prove that finally they have the House back again.