Vaccine distribution, pandemic data and a cross-party comity dominated today's virtual meeting between White House officials and a bipartisan group of 16 senators, Senator Angus King told Axios.

Why it matters: Given Democrats' razor-thin majority in both chambers of Congress, President Biden will have to rely heavily on this group of centrist lawmakers — dubbed the "Sweet 16" — to pass any substantial legislation.

• "If you were just listening on the call, I don't think you would have been able to tell who were the Republicans and who were Democrats and who were independents," said King (I-Maine).

Details: National Economic Council Director Brian Deese led the Sunday afternoon meeting, and several other top White House officials also joined the video call.

• It was the largest meeting between the Biden administration and senators since Wednesday's inauguration.

What he's saying: There's absolute consensus" that the administration and Congress' main priority needs to be speeding up the rate of vaccination, King said.

• The group plans to work closely with the White House to gather data about where the "bottlenecks" are in the current distribution system.
• King added that the senators asked for data to back up the administration's pandemic proposal. "You know, how did they arrive at the numbers that they have?"

One big question they need to solve, King said, is how much unspent money from the previous coronavirus packages can be reallocated to the Biden package.

Timing: King said that while the administration did not lay out a specific timeframe, there was general consensus that this next stimulus bill should be done sooner rather than later.

• However, looming in the background is the impeachment trial for former President Trump, which is roughly two weeks away.
• King said "it would be desirable" to start moving on the next relief package before then, but "whether that's going to be possible I just don't know."