WASHINGTON — President Joe Biden panned a Republican alternative to his $1.9 trillion COVID rescue plan as insufficient as Senate Democrats pushed ahead, voting to launch a process that could approve his sweeping rescue package on their own, if Republicans refuse to support it.

Biden and Treasury Secretary Janet Yellen joined the Democratic senators for a private virtual meeting Tuesday, both declaring the Republicans’ $618 billion offer was too small. They urged big fast action to stem the coronavirus pandemic crisis and its economic fallout.

Biden was likely to reiterate that message Wednesday as he steps up his public engagements with lawmakers on the issue. The White House announced that Biden would discuss the rescue plan with House Democrats by phone, followed by an Oval Office meeting with Democratic senators.

As the White House reaches for a bipartisan bill, Democrats marshaled their ever-slim Senate majority, voting 50-49, to start a lengthy process for approving Biden’s bill with or without GOP support. The goal is to have COVID-19 relief approved by March, when extra unemployment assistance and other pandemic aid expires.

“President Biden spoke about the need for Congress to respond boldly and quickly,” Senate Majority Leader Chuck Schumer said after the lunch meeting. “If we did a package that small, we’d be mired in the COVID crisis for years.”

The swift action from Democrats on Capitol Hill underscores the urgency of delivering Biden’s top legislative priority even as talks are progressing privately between Republicans and the White House, as well as with centrist Democrats, on potential changes to the package to win over broader bipartisan support.

Biden framed his views during the virtual lunch meeting with Democrats by talking about the need not to forget working and middle-class families — even those like nurses and pipefitters making $150,000 for a family of four — who are straining during the crisis, according to a person granted anonymity to discuss the private call.

The night before, Biden met with 10 Republican senators pitching their $618 billion alternative, and let them know it was insufficient to meet the country’s needs. The president made it clear that he won’t delay aid in hopes of winning GOP support.

While no compromise was reached during the late Monday session, White House talks with Republicans are privately underway.

The outcome will test the new president striving to unify the country but confronting a rising COVID-19 death toll and stubbornly high jobless numbers, with political risks for all sides. Vaccine distributions, direct $1,400 payments to households, school reopenings and business aid are all on the line.

Senate Republican leader Mitch McConnell criticized the Democrats for pressing ahead on their own. He said he had spoken to Biden ahead of his meeting with the 10 GOP senators.