Biden's meticulous approach to the presidency is intended to serve as a stark departure from the chaos of his predecessor, Donald Trump.
Two Democratic senators, Tammy Duckworth of Illinois and Mazie Hirono of Hawaii, condemned the lack of diversity in Biden's Cabinet.
AdDuckworth said she raised her concerns with the White House on Tuesday and she and Hirono threatened to withhold their votes on nominations until the administration addressed the matter.
Just before news of the Colorado shooting, White House aides leaked preliminary word about their next priority, a potentially $3 billion package with money for developing roads, hospitals, schools and green energy systems.
But for that program, like other legislative priorities, the White House faces tough prospects for any Republican support and would be forced to proceed along a party-line vote.