Russian Prime Minister Yevgeny M. Primakov faces a tough challenge on his Mar. 23 visit to Washington. He'll be asking the International Monetary Fund for $4.5 billion. Without some new funding, Russia may have to default on $17 billion in foreign debt payments that are due this year--or start printing masses of rubles. If the Russian request is denied, political turmoil could follow. A likely loser is Deputy Prime Minister Yury D. Maslyukov, Primakov's link to the Communists. Should he leave, the Communists will be less willing to cooperate and Russia's fragile political peace could be strained. President Boris N. Yeltsin recently met in his hospital room with reformer Grigory A. Yavlinsky, who is a leading candidate to replace Maslyukov as economic czar.