When the House of Representatives rejected all the alternative budget proposals last week, the country was denied the show of fiscal discipline it needs from government in order to have any chance of crawling out of this crippling recession. But if there is any solace to be found in the House's budget fiasco, it is this: the voters saw a clear demonstration of where the problem lies.

Part of it lies in President Reagan's stubborn resistance to a "mid-course correction" in his own policies--a resistance that inhibits most of the congressmen of his own party from supporting any such change.

But a larger problem is the inability of the Democratic Party to forge an internal agreement on an alternative to Reaganomics.

The House was, as always, a near-perfect reflection of those external realities. By March of this year, Washington Post- ABC News polls showed a shift in public opinion from the earlier broad support of Reagan's policy. By a 2-to-1 margin, those polled said Congress should make "substantial" changes in Reagan's budget. A follow-up poll in April found most saying his tax cuts and domestic spending reductions were too deep.

The House votes last week reflected that judgment. First, a majority amended the Reagan-endorsed budget to shift $4.8 billion from defense to health care--a straight-out Medicare vs. military test. Then, the House rejected the overall Republican plan, which still sacrificed domestic spending to defense needs and the scheduled tax cuts.

There were cheers from the Democratic majority on that vote, for never once in all of 1981 had they been able to derail the president's legislative express train.

But the cheers were short-lived. Having cleared the agenda, at least temporarily, of Reaganomics, the Democrats then failed, on three tries, to find a majority for any plan of their own. They could not muster a majority for a plan devised by five of their brightest young members, in conjunction with a handful of moderate Republicans. Nor could they unite behind either the original or a modified version of the Democratic budget reported by the House Budget Committee and presented by its chairman, Rep. James R. Jones (D- Okla.).

In failing to meet their legislative responsibilities, the House Democrats confirmed another finding of that March poll. The voters--who are rarely fooled-- said that as far as they could see, the Democratic alternatives were not better or worse than Reaganomics; there were no alternatives at all.

It was an abject and embarrassed bunch of Democrats who shambled out of the Capitol in the small hours of Friday morning, when the last of the budget-wrecking was done. Echoing in their ears were the words of Speaker Tip O'Neill: "When Americans wake up and find that Congress did not do its job, what frustration there will be."

In the corridor, Rep. Bill Alexander of Arkansas, the chief deputy Democratic whip, made the obvious political point. "Reagan is going to murder us," he said. "We had him on the run, when we could say his budget had failed the country. But now he can say the failure is the Democrats', because we were unable even to produce an alternative."

The seriousness of the failure is heightened by the fact that, this time, the Democrats really did give it their best shot. Rep. Richard Bolling of Missouri, perhaps their most skilled parliamentarian, devised rules for debate designed to give every faction in the party a clean vote on its pet provision--in hope they would support, and not disown, the final product. The agenda guaranteed the Democrats would have the last chance to assemble a majority.

That they could not do so shows how politically divided and intellectually bankrupt they really are. They are worse off, in both respects, than they were a year ago, when Reagan was riding high. Last spring, the Democrats were able to get 176 of their members to support the Jones budget against Reagan's preferred plan. This year, Jones could muster only 171 votes for his product.

Last week, the defections came from both ends of the Democratic spectrum-- not just the conservative wing. Barely half the 63 Democrats who voted against the Jones budget were southern "boll-weevils." Most of the black Democrats--angered by what they regarded as inattention to their own budget proposals--also balked, as did a dozen or so white liberals.

The conventional answer of Democrats is to say that if only they had more members in the House, they would do better.

But the voters will not be satisfied with that. They will want to know: do what?

That question ought to be at the top of the agenda for the Democratic Party's mid-term mini-convention in Philadelphia at the end of this month. Reaganomics is in trouble. But Democrats still have to learn that you can't beat something with nothing.