The nation’s governors heard hopeful reports on two of the most important concerns of their constituents--the health of the U.S. economy and relations with the Soviet Union. Both Alan Greenspan, chairman of the Federal Reserve Board, who indicated that he expects the country to avoid a severe recession, and Sen. Bill Bradley (D-N.J.), who said that success for President Mikhail S. Gorbachev’s program would lead to Soviet military cutbacks, hedged their forecasts with caveats and caution. At the meeting of the National Governors’ Assn. in Chicago, Greenspan said that Americans need to save more of their income to provide funds for investment in new technology. Bradley pointed out that Gorbachev faces serious difficulties in restructuring his country’s economic and political system.