WASHINGTON — Democrats are preparing to bypass Republican objections to speed President Biden’s $1.9 trillion economic aid package through Congress, even as administration officials and congressional moderates hold out hopes of passing a bill with bipartisan support.

On a day when new Commerce Department data showed that the economic recovery slowed down at the end of last year, Democratic leaders in Congress and administration officials said on Thursday that they would start a process next week that would allow the measure to pass with only Democratic votes. Behind closed doors, congressional committees are already working to turn Mr. Biden’s plans into law.

Party leaders remain hopeful that Mr. Biden can sign his so-called American Rescue Plan into law by mid-March at the latest, even with the competing demands of a Senate impeachment trial of former President Donald J. Trump, which is set to begin the week of Feb. 8.

“We want it to be bipartisan always, but we can’t surrender if they are not going to be doing that,” Speaker Nancy Pelosi of California said at a news conference on Capitol Hill.

“I do think that we have more leverage getting cooperation on the other side if they know we have an alternative as well,” she added.