The White House on Thursday signaled it could throw its weight behind passing President Biden's coronavirus relief package via the budget reconciliation process, arguing that doing so would not preclude the vote from being bipartisan.

Administration officials have been peppered with questions in recent days about whether Biden would support reconciliation, which would allow the bill to pass with a simple majority in each chamber, as Republican senators express opposition to key parts of the president's $1.9 trillion measure. Passing the legislation without reconciliation would require support from at least 10 Senate Republicans.

"The president wants this to be a bipartisan package regardless of the mechanisms. Republicans can still vote for a package even if it goes through reconciliation," White House press secretary Jen Psaki said during a briefing with reporters. "There’s no blood oath anybody signs. They’re able to support it regardless."

Psaki would not speculate on whether Biden would back a bill that passes with no Republican support given his frequent calls for unity and bipartisanship, but said the president is having regular conversations with members of both parties to get the bill passed.

"He wants this to be a bipartisan package," Psaki said. "He’s listening to Democrats and Republicans — we all are — to ensure that’s what it looks like at the end of the day."

Psaki's remarks came hours after Senate Majority Leader Charles Schumer (D-N.Y.) warned that Democrats were willing to go it alone on the coronavirus relief package, potentially starting the process as soon as next week.

"The dangers of undershooting our response are far greater than overshooting ... so the Senate as early as next week will begin the process of considering a very strong COVID relief bill," Schumer said from the Senate floor.

Psaki and other White House aides made clear earlier Thursday that the administration would not break up the legislative proposal to pass it piece-by-piece.