Most of the headlines produced by Pope John Paul II's eight-day visit to his native Poland stressed his criticism of the Polish government and his affection for the now outlawed Solidarity movement in Poland.
But much more important to the future is the fact that the visit began and ended with a private session between the Pope and the head of the Polish government, also head of the Polish communist party, Gen. Wojciech Jaruzelski.
At the end of the second of these two private sessions an official communique stated the following:
''The hope was expressed that the visit will contribute to the peaceful and favorable development of social life in Poland and the strengthening of peace in the world. It was also recognized that further contact between the Apostolic See and the Polish United Workers' [Communist] Party will serve the good of the State and the Church.''
Add that the official head of the Polish state, Henryk Jablonski, was present at the Krakow airport for the Pope's departure. The two chatted amicably together. There was nothing controversial in the farewell remarks.
Add that in advance of the papal visit to Poland Izvestia in Moscow printed a barbed attack on the Polish government which clearly was aimed at General Jaruzelski and hinted at a Kremlin desire to see him brought down and replaced by a more hard-line com-munist.
Add one final item to the list of facts which clarify the meaning behind the visit.
On the second day of the Pope's return to Rome the semi-official Vatican newspaper L'Osservatore Romano carried an article declaring that Lech Walesa ''has lost his battle.'' Within hours, that same day, the author of the article, deputy editor the Rev. Virgilio Levi, was dismissed from his post but what he had written was not repudiated.
In other words, an extremely interesting and a possibly fateful negotiation has now begun. The Roman Catholic Church will negotiate with the communist leadership of Poland over the possibility of an arrangement under which martial law would be lifted and civil law would return to Poland. In return the Polish people would cooperate in a national effort to regain economic solvency. The church would contribute to the peaceful arrangement by using its good offices in Washington to gain a resumption of normal commercial relations between Washington and Warsaw.
It will be an extremely delicate negotiation. Lech Walesa had to be excluded at the outset. The general can negotiate with the Pope who is head of a sovereign state (Vatican City) and head of a major world religion. The general cannot negotiate (and also keep his job) with a Polish citizen heading a political movement which in its heyday very nearly became the unofficial political power in Poland.
The stakes are high. The Pope is working for a bloodless arrangement under which the lot of the Polish people will be eased. If he fails, the result will be revived strain and tension which would certainly mean more repression, more bloodshed, and continued economic weakness. Such a condition could all too easily lead to civil war ending in a takeover of Poland by Soviet armed forces.
During the visit the Pope spoke with deep emotion about the present sufferings of the Polish people, but he also spoke of ''the enormity of suffering, torment, and tears which have successfully been avoided.''
Obviously, in his mind the lesser evil for Poland is to suffer the present government of Poland, deal with it cooperatively, and gain time for the Polish people. It is not the ideal. As a Pole the Pope obviously yearns for the total freedom of Poland. But he would rather do business, if he can, with General Jaruzelski than see Poland once again overrun by foreign soldiers and put into a condition of virtual vassalage.
The Pope left Poland on June 23. Three days later Zbigniew Brzezinski, Polish-born, a Roman Catholic, and national security adviser to former President Carter, urged that Washington ''lift some sanctions immediately so that Jaruzelski and company can claim some credit.'' Without such a signal from Washington Mr. Brzezinski thinks that ''Jaru-zelski will be under pressure from hard-liners . . . and from the Soviets to reaffirm strict ideological conformity and maybe crack down even further.''
Will Washington support the Pope's efforts for a peaceful resolution of the Polish crisis?