Gov. Arnold Schwarzenegger, yielding no ground to Donald Trump, has been putting his own stamp on the art of the deal.

As the mid-May deadline approaches for the governor to present a revised budget, Schwarzenegger is not only putting it in finished form, he's getting buy-in for budget cuts from those most affected, such as educators and local officials.

Is Schwarzenegger, in a refreshing change, going the extra mile by not just writing up a budget but doing the hard work of selling the necessary cutbacks?

Or is he trying to elbow the Legislature out of the picture by presenting it with a budget deal that it can't change without upsetting too many important constituencies?

As in so much of politics, you can read it however you please, but in my view, the Legislature should be more grateful than indignant.

In January, Schwarzenegger struck a deal on K-12 education. Schools would accept $2 billion less than the state funding formula mandates, in return for a higher funding base in years to come.

Now he's talking with local governments. They're pondering a cut of $1.3 billion the next two years. The governor would support a constitutional amendment to end state raids on local funds.

Higher education looks to be next in line for cuts in the near term, restoration of stable funding later on.

It should be no surprise by now that Schwarzenegger has brought energy and purpose to a faltering process, as he did with the stalled workers' compensation debate. His most important accomplishment has been to get acceptance for the kinds of cuts that virtually everyone in the Capitol thinks are necessary, but which seem not to happen.

The governor's style is appreciated even by those who are feeling the knife. Chris K. McKenzie, executive director of the League of California Cities, recalls a year when Gov. Gray Davis proposed to cut $3 billion from local government, and ``he never even discussed it with us.'' Schwarzenegger has introduced ``a different way of doing business, one that we welcome.''

No process is without drawbacks, however. As Schwarzenegger works his way through the budget, first K-12, then local government, then higher education, the remaining segments, health care and welfare, might be left out. The last to be invited to the table could find nothing but scraps to bargain over.

Looking long term, Schwarzenegger must avoid the pitfall that these deals of ``pain now for promises later'' might leave the state with more promises than it can keep. The Legislative Analyst's Office forecasts that the state faces ongoing annual budget deficits of $7 billion.

These are dangers the Legislature must watch out for, which brings us to the other major possible pitfall of Schwarzenegger's approach -- annoying the Legislature by leaving it out.

First, though, consider why the Legislature might not mind. Getting to write the budget in times like these is not exactly an honor. The Legislature's Democratic majority might be relieved to be handed a budget in which the unpopular cuts have already been accepted by the groups that will have to absorb them.

But the state Constitution gives the Legislature a major role in writing and passing the budget, which legislators themselves would be the last people to dismiss. Schwarzenegger won't make them happy if he delivers a budget with a note that says: ``Please read and initial.''

At least some Democrats dislike the substance of the deals. They think the teachers union or university officials might be chickening out, so afraid they'll get a deeper cut if they don't deal that they are selling students short.

The deals seem to take for granted Schwarzenegger's unwillingness to raise taxes. ``We would not have to cut these things,'' says one Democratic legislator, ``if he had not eliminated vehicle license fees,'' a move that cost the state $4 billion.

So there will be some grumbling, but it's unlikely to carry the day. Getting a budget passed has been so painful the last couple years, that the life preservers will be grabbed with gratitude, even those tossed by a governor of the opposite party.