Last week it was Egypt's Hosni Mubarak. This week it will be Jordan's King Hussein meeting at the White House with Ronald Reagan. Later in October he will be followed by the top men of Israel's government of national unity, Deputy Prime Minister Yitzhak Shamir, and then Prime Minister Shimon Peres.

They are all key players in the only Middle East "peace process" in sight: a difficult and delicate series of maneuvers by Hussein designed to resolve the deadlock over Palestinian representation in any direct Israeli-Jordanian negotiations.

It's a murky, messy business, full of symbols as well as substance. If there is a shared sense of urgency, there are also deep divisions centering on Hussein's need for a semblance of association with the Palestine Liberation Organization and Israel's insistence that no PLO hand can be allowed to show. But as recently as last May, when Hussein was in town, the Reagan administration thought Hussein's convoluted course of action was at least worth encouraging.

So what could possibly be wrong with using American influence now to give the whole process another nudge? Nothing, I would argue. It would not be the first time the United States stepped in to push or prod to good purpose without having any tidy end result in mind. Sadat's celebrated breakthrough to Jerusalem was balanced by a peace proposal so negative in tone that only energetic intervention by the Carter administration could have gotten that initiative back on track.

"Peace is a process," Henry Kissinger was fond of saying when he was in charge of the process. The underlying assumption -- that the absence of any movement toward peace in the Middle East is acutely dangerous -- seemed to make good sense at the time.

But not now -- not even to Kissinger, who is counseling a long look before the United States leaps into the Middle East again. Without a clear objective, Kissinger argues, U.S. meddling can only make things worse. Former U.N. ambassador Jeane Kirkpatrick heaps scorn upon the "U.S. Department of State" for its efforts to promote negotiations, as if her former boss in the White House was somehow not involved.

The thunder from the right is stoutly reinforced from the left in Congress. There, Democrats (and some Republicans) responsive to the Israeli lobby are busy robbing the U.S. government of useful influence by attaching all kinds of mischievous conditions to the arms aid Reagan would make available to the so-called moderate Arabs.

The president, in his meeting with Hussein, must weigh not only the current state of Hussein's efforts but also how much effort and political capital he himself is prepared to spend.

Finally, he will have to weigh the considerable risks of applying the right's doctrine of benign neglect to the new violence erupting on the West Bank -- and the chain reaction it could trigger. "We have entered a new phase of locally generated resistance," Meron Benvenisti, a recognized Israeli expert, recently told The New York Times. "It is not organized by cells or by the PLO."

Yet Israeli authorities require a culprit -- in this case not simply the PLO, but Hussein for harboring a PLO headquarters in Amman. Hence the loaded warning to Hussein a week or so ago from defense minister Rabin of unspecified "dangers" if the West Bank security situation continues to "deteriorate." The echoes of the prelude to the Israeli invasion of Lebanon are not lost on Middle Eastern and American experts alike, the more so since Rabin is not given to reckless threats.

Continuing unrest on the West Bank plays into the hands of Israel's right-wing hard-liners, already gaining in strength, and increases the pressure for Israeli reprisals. It is not a happy choice either way you look at it: violence capable of swirling out of control on the one hand, and a faltering, perhaps even flawed "peace process" on the other. But as between the two, the question is not even close.

Before we take the Kirkpatrick way out -- "we are not party to the conflict" -- it is worth remembering that one way or another we have been party to every outbreak of Arab-Israeli hostilities.

Before we become a party once again to the consequences of doing nothing -- or too little, too late -- where is the comparable danger in being a party to trying to keep a "peace process" alive?