President Obama and congressional Republicans groped today for a compromise to avert an unprecedented US default and end the 10-day-old government shutdown. "We expect further conversations tonight," House Majority Leader Eric Cantor said cryptically at nightfall, after he, Speaker John Boehner and a delegation of other Republicans met for more than an hour with Obama at the White House. The White House issued a statement describing the session as a good one, but adding, "no specific determination was made." Yet it seemed the endgame was at hand in the crises that have bedeviled the divided government for weeks. Both sides expressed fresh hopes for a resolution soon.