WASHINGTON — Congressional Republican leaders and White House officials on Monday explored ways to resurrect trade legislation that stalled last week when House Democrats objected and dealt President Obama an embarrassing defeat at the hands of his own party.

In meetings at the Capitol and in telephone conversations with Mr. Obama and administration officials, lawmakers ticked through a list of complicated procedural options that could circumvent House Democratic opposition to granting the president the power to expedite trade deals.

As they examined the possibilities, House Republicans took steps Monday night to give Speaker John A. Boehner until the end of July to try again to win approval of a bill to aid workers displaced by global trade agreements, a measure that was tied to the package that would give Mr. Obama so called fast-track authority to advance trade negotiations. The extension could be under vote on Tuesday and showed that the trade fight was far from settled.

Led by Representative Nancy Pelosi of California, the party leader, most House Democrats last Friday opposed the worker aid — something the party has backed for four decades — leaving the fate of the president’s ambitious trade agenda tenuous.