Although George Shultz tried to dismiss Jim Wright's breathless invasion of President Reagan's Nicaraguan policy as a ''tiff,'' the chasm between the ambitious, artful speaker and the gravely weakened Reagan will widen in the dying days of the administration.

Wright's surge into the heart of the president's foreign policy prerogatives is no aimless search for momentary headlines. It is a serious reach for influence that no speaker has ever attempted in the foreign policy arena.

His activities are not limited to Nicaragua. Wright pushed for Mikhail Gorbachev to speak before a joint meeting of Congress next month when the White House asked for guidance. While congressional Republicans are disgusted, the White House saw gains if Reagan gets reciprocal treatment in speaking to the Soviet people. But Wright played a key part, overriding how it would look for Congress to bestow so high an honor on the leader of international communism as the war in Afghanistan worsens.

The speaker is succeeding in his immediate objective: to cut the heart out of the president's Nicaraguan policy. That heart is using the contras as the only lever available to the United States to compel Daniel Ortega and his Sandinista regime to democratize their dictatorship and hold genuinely free elections in 1990.

Wright's artful ways, becoming a legend on Capitol Hill after a mere year as speaker, played like political poetry on Thursday, Nov. 12. On that day, he casually dropped word to Secretary of State Shultz, visiting the speaker's office, that Ortega was planning to unveil a new peace plan the next day.

That Wright knew so much more than Shultz himself somewhat surprised the secretary. But he simply counseled the speaker on how important it was to keep the United States out of the negotiating process until Ortega presented a fair proposal to the contras. The administration wants the United States to stay on the sidelines for now and let the Nicaraguans and their Central American partners do their stuff.

Wright apparently did not think it worthwhile to mention to Shultz that Ortega himself -- bringing along the Nicaraguan mediator, Cardinal Miguel Obando y Bravo -- would be dropping in to his office the next day. Nor did he leave even a hint that the new peace plan -- he called it a ''package'' -- would become public as a result of that session.

When a wire service story was put on his desk late Thursday evening, Shultz learned about that meeting where the Ortega ''peace'' plan would be unveiled. Hurt and angry, he felt compelled to cancel his own meeting Friday morning with the cardinal to avoid appearing as a ''participant'' in Ortega's manipulations. On Friday, Wright sweetened the pot for Ortega by offering to name ''mediators'' from the United States to help the cardinal.

The true extent of the speaker's involvement in Ortega's brand of peace-making probably came in an account in the pro-Sandinista Managua newspaper, El Nuevo, on Monday. It specifically credited Wright with helping Ortega ''finalize'' the 11-point peace plan. Wright, said El Nuevo, persuaded the Sandinista leader to remove four of the original 15 points in order to sweeten the package for skeptics in Washington.

El Nuevo may have been playing with the truth in giving Wright so much credit. That would be par for the Sandinista course during Ortega's sensationally successful Washington visit last week. He used Wright as a key, opening doors to give himself respectability and sincerity in the search for peace.

But the plan Ortega offered, and that Wright apparently underwrote, dooms the contras. It would barricade them into three small areas away from their strongholds. After being disarmed, they would be disbanded. If they refused, Sandinista forces could annihilate them. Wright, who has never once supported any help for the contras, and other anticontra members of Congress would make sure no aid was passed to revive the guerrilla army.

Jim Wright backed down a bit when he asked his friend and fellow Texan, Democratic elder statesman Robert Strauss, to intervene with Shultz in the interest of ending their little ''tiff.'' But the speaker, who has assigned the tough task of budget negotiations to Majority Leader Tom Foley while he plays in the glittering game of nations, is most assuredly not backing down.

Slamming his fist on his desk, he told a colleague last summer he would not let President Reagan ''get away with'' funding the contras and, in Wright's terms, trying to topple the Sandinista government by force. Last week he showed how much he meant it.