The Associated Press / President-elect Joe Biden campaigns in Atlanta Monday for Senate candidates Raphael Warnock, center, and Jon Ossoff, left.

This story was updated Wednesday, Jan. 6, 2021, at 10 p.m. with more information.

It appears Vice President-elect Kamala Harris won't be moving very far.

Having spent four years of a single term in the United States Senate, she's likely to be in that chamber of the U.S. Capitol frequently over the next two years since the body will be split 50-50 with the election of Democrats to both Georgia seats in runoff elections Tuesday.

The Rev. Raphael Warnock, an Atlanta minister, was declared the winner in the state's runoff election, defeating Sen. Kelly Loeffler, who was appointed to the seat by Gov. Brian Kemp after Republican Sen. Johnny Isakson stepped down in 2019 due to ill health.

Jon Ossoff, a documentary filmmaker with one of the lightest resumes for a Georgia senator in recent history, eventually was declared the winner over first-term Sen. David Perdue by some 29,000 votes (about .66% of the total vote), barring any recount or unforeseen challenge.

READ MORE: Warnock, Ossoff win in Georgia, handing Dems Senate control

Democrats, by virtue of having one of their own in the White House, will control a split Senate, with Harris being able to cast the deciding vote in cases where the 50 Republicans vote one way and the 48 Democrats (plus two independent who caucus with Democrats) vote the other way.

Senate Minority leader Chuck Schumer, D-New York, will become majority leader and as such will decide committee assignments.

The last time a 50-50 Senate occurred, in 2001 with Republican George W. Bush as president, Republicans agreed to a power-sharing agreement with Democrats, where, among other things, all committee had equal numbers and minority members could serve as presiding officers of the Senate.

Don't look for Schumer to be as magnanimous as Republicans were 20 years ago. The Democratic Party has slid to the far left since then, and Congress is a much more ruthless place to be.

Perdue and Loeffler, and President Donald Trump, campaigned that the election of the two Georgia Democrats would result in a socialist agenda being passed by Democrats once President-elect Joe Biden is inaugurated.

To be sure, Democrats — with Harris breaking ties — can have their way on many issues for at least two years, assuming they can get the vote of each member who traditionally votes with them. However, unless they eliminate the cloture rule (requiring 60 votes to end debate on most measures), their ability to pass radical legislation will be limited. And one Democrat, Sen. Joe Manchin of West Virginia, has said he would not vote to eliminate the cloture rule.

The tie may put Biden in a bind, however. Since Democrats conceivably could pass legislation by eliminating the cloture rule, the dominant left wing of their party may push to do just that. If they do pass such legislation, any plans Biden may have to work with Republicans will be lost. And that will increase the chances Democrats will lose both the House (which they will control during this session by a slim 10-12 votes) and the Senate in 2022.

It will be an interesting process to watch.