WASHINGTON - The Democratic Party became the majority party in the US Senate on Wednesday after Vice President Kamala Harris swore in three Democrats as new members of the upper chamber.

Stepping onto the Senate floor for the first time as vice president of the United States -- thus president of the Senate -- Harris swore in Jon Ossoff and Raphael Warnock from Georgia, as well as her replacement from California, Alex Padilla.

The party breakdown in the Senate is 50-50 now, with Harris having the power to cast the tie-breaking vote.

Warnock, 51, and Ossoff, 33, won runoff elections in Georgia earlier this month that determined the control of the Senate. Padilla, 47, was picked by California Governor Gavin Newsom to fill Harris's Senate seat when she resigned to become vice president.

Meanwhile, Democratic leader in the chamber, Chuck Schumer, became the Senate majority leader. "We have a lengthy agenda, and we need to get it done together ... This will be an exceptionally busy and consequential period for the United States Senate," he said in the first speech in his new role.

"The divisions in the country are real. We have no choice but to try to work together every day," Schumer said in remarks to Republican senators.

Mitch McConnell of the Republican Party became the minority leader. Schumer and McConnell will have to reach a power-sharing deal in the coming weeks on how the business of the Senate will be run, with issues remaining to be resolved including the number of senators each party will have on committees and the mechanism to break ties in the panels.

McConnell in a floor speech noted Joe Biden, who was sworn in as the 46th president of the United States earlier in the day, "made unity the major thing of his inaugural address," acknowledging that both Biden and Harris are alumni of the Senate and pledging cooperation with the new president "wherever possible."

The Democrats have now controlled the White House, the Senate and the House, but the evenly-shared senate seats and the shrinking majority they have in the House -- the slimmest in decades -- show just how divided the country is.