THIS UNFORTUNATE coal strike is now approaching an unfortunate conclusion. The Carter administration is desperate to get the thing settled. It is not only the threat of a spreading power shortage; the strike has also become an excruciating political embarrassment to the president. He brought the negotiations into the White House with a grand gesture, and there they have stuck. By this time there have been too many headlines hinting at dramatic breakthroughs -- followed by no visible progress. The White House has now arrived at the same conclusion as everyone else: There is no rational solution that can be achieved quickly. Since the White House needs a quick solution, it is sliding toward a settlement that will do nothing about the epidemic of wildcat strikes that has increasingly disrupted production and disrupted the miners' health and pension funds.

That kind of a settlement would be a severe setback to the president's own energy plan with its emphasis on more coal. But when a president gets into trouble, the short-run necessity usually triumphs over the long-run interest. We have to acknowledge that none of the various legal solutions -- court orders, new legislation -- holds any promise. The basic fact here is that the union is in the grip of a populist rebellion that is determined to preserve the unauthorized local strike as its only reliable weapon against companies, arbitrators, judges and its own national leadership -- all of whom it regards with mistrust varying only in degree.

Earlier this month the United Mine Workers' leadership settled with the coal companies on a contract that would have imposed severe sanctions on wildcat strikes, in return for an array of financial benefits. That is the contract that the UMW's bargaining council immediately rejected. Subsequently a small company, Pittsburg and Midway Coal, bargaining outside the industry association, signed a contract in which the wildcat clauses were very heavily diluted. The union's bargaining council approved that one. The administration's strategy now is to make the rest of the industry swallow the P and M contract whole.

The governors of several coal-producing states met with Mr. Carter at the White House yesterday, and called loudly on the other companies to accept the P and M terms. The president's special representative for foreign trade, robert Strauss, has been telephoning major steel companies to warn them that the administration will permit rising steel imports if production here falls. the steel companies' captive coal mines will be influential in any coal-industry settlement.

This whole sequence of events is, in a sense, the effect of too sudden a rush of prosperity toward people too long neglected and denied. For decades both the miners and the companies believed, with good reason, that they were in a dying industry. Prices were low. Employment in the mines fell rapidly and steadily. Management generally practiced the shortsighted and coarse labor relations of declining industries. The miners felt themselves to have been forgotten and left behind by the rest of the country.

Then, all at once, the country needed coal. In a few years the price tripled, and new jobs opened up in mining. A new president declared that coal would be the salvation of the country. Both miners and companies glimpsed the pot of gold at the end of the rainbow. The surge of new hope and new expectations was too great a weight for the union structure or the bargaining process to bear. Both have now collapsed. Perhaps, in the present circumstances, there is no alternative to a contract sending the miners back to work with a lot more money and no real sanctions against more wildcat strikes. But it is necessary to recognize that there is a price. The administration is sacrificing its energy policy to the necessity of ending the strike quickly. Secretary of Energy James Schlesinger needs more coal production. But Secretary of Labor Ray Marshall has to get these labor negotiations wound up, and he's in a hurry. Mr. Schlesinger, meet Mr. Marshall.