THE Chechen and Ingush peoples of the northern Caucasus region of Russia learned by watching the larger republics that have broken away from the Soviet Union. In late October, they elected their own president - a fiery nationalist and ex-general named Djokhar Dudayev - and asserted their own independence.Russian President Boris Yeltsin at first tried to crack down. He declared a state of emergency and dispatched a few thousand KGB troops toward the tiny breakaway "autonomous republic." That repulsed Mr. Yeltsin's liberal supporters in the Russian Parliament. They accused him of using the same heavy-handed tactics that caused so much trouble in the Baltics and in Georgia. Their concerns were justified. Military action against the Chechen - a people known for tenacity in battle - could, as one member of Parliament put it, become "another Afghanistan." Beyond that, negotiations are much more in line with Yeltsin's professed principles. He recently attempted to mediate the snarled dispute between Armenia and Azerbaijan. Chechen-Ingush gives him a chance to apply diplomacy within his own huge, polyglot republic. It's not clear, however, that Mr. Dudayev is open to talk. Still, an arrangement that would keep the little republic within the Russian federation while granting it expanded self-rule is logical. An independent Chechen-Ingush, with its 7,450 square miles (about the size of New Jersey) and 1.3 million people, has doubtful viability. Russians are concerned that bigger, more centrally located chunks of their republic - notably Tatarstan - might push for independence too. A negotiated political resolution to the Chechen-Ingush problem could be a warm-up for greater challenges just down the road. All this arises as the Russian leader is attempting to implement radical economic reforms in the face of growing public discontent and the arrival of winter. Somehow the argument for free-market reform - that it holds the only hope of long-term prosperity - has to be effectively joined with the argument for continued federation. This task could be a make-or-break test for Yeltsin and his reformist colleagues.