IT IS an extraordinary political life sign for President Carter that he should have recruited Sen. Edmund Muskie to become secretary of state. Whatever else the resignation of Cyrus Vance had done, it had contributed to a national and perhaps even international sense that the administration was hanging on by the skin of its teeth. Mr. Carter had a desperate need to convey that he had not surrendered to events. By reaching out beyond his immediate political family to a senior senator, one commanding high respect in Washington and the country and known favorably abroad, the president has provided evidence that he means to last the storm through. The peril to the Carter administration is still there, but beyond question the Muskie nomination helps to tame it.

In accepting his new appointment, Mr. Muskie claimed no special preparation beyond having had the foreign policy exposure of a senator for 22 years. Though he is not known as an ideologue and has not taken a central part in recent policy debate, he is generally identified -- from past positions on the Vietnam War and strategic arms control -- as being more at home at the Vance end of the spectrum. How these views, taken from an earlier congressional context, will translate into the top executive-branch foreign policy job now is uncertain. The policy requirements he briefly underlined yesterday were stability and strength. He also observed, aptly, that it is a time of risk and that the American sense of purpose is widely questioned. These statements suggest a sensitivity to the special demands of the current situation. Mr. Muskie is being taken aboard to add seriousness and a politician's seasoned judgment to a troubled administration. That he is quite aware of the demands upon him was indicated by his confident assertion that the president has left no doubt that he, Edmund Muskie, will be Mr. Carter's foreign policy spokesman.

In finding a secretary of state, however, Mr. Carter is incurring a substantial cost to his economic policy. Mr. Muskie has been the crucial figure in defending the integrity of the budget process in the Senate in the midst of a soaring inflation, a recession and a presidential campaign. As chairman of the budget committee, he has brought his considerable personal qualities to the endless struggles to force the committees to stay within the Senate's spending limits. Only an international crisis of the current dimensions could have justified his move to the Department of State.