This week the Democratic-controlled House Budget Committee is supposed to get down to work on drafting the Democrats' version of the fiscal 1987 budget. For the past month, President Reagan's budget has been the only one out there, and Democrats have had a field day complaining about its deep cuts in domestic programs and steep boosts in defense spending.

Now the Democrats have to frame their alternative, and the country will get a chance to measure whether they put partisan advantage or public responsibility first. They are divided at the top, but the prevailing view "tips" them toward partisanship and away from responsibility.

The oft-reiterated view of retiring House Speaker Thomas P. (Tip) O'Neill Jr. is that revenues are needed for any equitable solution to the deficit dilemma, but that any tax increase must be initiated by President Reagan.

That view is echoed by Budget Committee Chairman William H. Gray III (D-Pa.) and is likely to prevail. But it is not the view of House Majority Leader Jim Wright, the man who likely will succeed O'Neill as speaker next January. In an appearance before the National Governors Association last week, the Fort Worth congressman said that those like himself who don't want to reverse the defense buildup and don't want to slash education and health spending ought to be ready to pay for them.

"If that takes a tax increase," he said, "so be it."

The division between O'Neill and Wright is more one of tactics than of substance -- but it is vital in the current circumstance. Senate Republicans, led by Majority Leader Bob Dole and Budget Committee Chairman Pete Domenici, are prepared once again to take the political risk of defying Reagan's threat to veto any tax increase, in order to frame a balanced and responsible budget resolution.

But the House Democrats are preparing to abandon the course of responsibility and let the country live with the crippling effects of the Gramm-Rudman-level defense and domestic program cuts.

Wright is not going to push the issue against the man whose job he covets. After his appearance before the governors, he told me, "Early last year, a decision was made of which I only later became aware. The speaker promised Danny Rostenkowski (the chairman of the tax-writing Ways and Means Committee) that he would support a revenue-neutral tax- reform bill. . . . That is still the speaker's policy, and I am not going to create a mutiny. That's not my style."

There is more to Wright's pointed dissociation from the policy than meets the eye. Rostenkowski is a potential, if long-shot, rival for the speakership, and the tax-reform bill Rostenkowski pushed through the House last year over Wright's opposition is not liked by Wright's business and energy-industry constituents.

But there is a fundamental issue of Democratic policy and politics that Wright has raised -- even if he will not push it aggressively.

The Democrats know that, twist or turn the budget as they will, both the national defense and important human-service, farm and urban programs are going to get hurt unless -- as Domenici says -- $12 billion to $20 billion in new taxes are added to the 1987 budget mix.

Why won't they advocate what they know is needed? There are two answers. Many of the House Democrats point to Reagan's battering of Walter F. Mondale in the 1984 election, after Mondale boldly declared that taxes would have to go up to solve the budget crisis. They ask: Why set Reagan up for a veto and a "make my day" speech accusing the Democrats of being inveterate taxers?

The weakness of their argument is that Senate Republicans -- who are far more vulnerable this year than most House Democrats -- have regularly taken the lead since 1982 in advocating responsible tax and budget policies despite Reagan's posturing.

The second -- and real -- reason House Democrats dodge the tax question is that many of them have concluded that their party cannot regain power until more voters feel real pain from the Reagan-imposed budget cuts.

One of O'Neill's close associates told me, "Our strategy is to be sure the Republican Party has its name emblazoned on every program cut. . . . It may take more than a few months for the middle-class families to feel the painful effects, but inside two years, they will know the price of supply-side politics."

That may prove true by 1988. But meantime, Democrats are going to acquiesce in cuts that jeopardize defense, deny education opportunities and health protections and eliminate many of the basic tools for future economic growth and competitiveness -- by turning their backs on the modest tax increases that could prevent this budgetary carnage.

Jim Wright is not wrong when he dissociates himself -- however cautiously -- from what is truly irresponsible politics and questionable leadership in the only part of the national government the voters have left in Democratic hands.