The 2020 election was about as bad an outcome as was possible without it being a loss.
Joe Biden, when the paperwork is finished, will be the President-Elect, and Kamala Harris will be his Vice President on January 20, 2021, despite President Trump's protests to the contrary.
It is possible that his total number of electoral votes will be the bare minimum 270 with the marginal state won by the narrowest of margins. It could be as much as 306, depending upon the outcome of final counts in Pennsylvania and Georgia. His popular vote margin is currently about 3 million out of 136 million. Total turnout was 160 million and Biden's popular vote margin will improve as more votes are counted.
Joe Biden's DW-Nominate score when he left the U.S. Senate during the 2009-2011 session of Congress (the 111th) was -0.314, which was to the right of Warren and Sanders, and to the left of Gabbard and Klobuchar.
Kamala Harris is more progressive than at least 85-90% of the Senate. But, of course, a Vice President has little formal power and usually exercises that power at the direction of the President.
The Republican Controlled Senate
Democrats will start the 117th Congressional session on January 3, 2021 with 48 Senators (including independents who caucus with them) while Republicans will have 52.
A runoff in a Georgia Special Election to fill a vacancy currently filled by a Governor appointed Republican will be held on January 5, 2021 and could shift the balance from 48-52 to 49-51.
Either way, the Republicans will be in control unless a moderate Republican like recently re-elected Senator Susan Collins (R-ME) can be convinced to change parties and Democrats win the runoff election (or can win over another party switcher). She is the most moderate Republican in the U.S. Senate; Lisa Murkowski (R-AK) is the second most moderate member of the GOP caucus in the Senate.
Of course, even if the Democrats could somehow achieve a 50-50 split, which together with the Vice President would give the Democrats control of the Senate, this majority would still be subject to defections from the turncoats and from conservative Democrats in the U.S. Senate such as Joe Manchin III (D-WV), the most conservative member of the Democratic caucus in the U.S. Senate.
The Democratic Party Controlled House
Democrats will have a slightly reduced majority in the U.S. House which they still control. It isn't clear if Nancy Pelosi will retain her leadership position as Speaker of the House, or will be replaced with new leadership.
The U.S. Supreme Court will have a 6-3 conservative majority. Four far right conservatives (Thomas, Alito, Barrett and Kavanaugh), two plain old conservatives (Gorsuch and Roberts) who will hold the swing votes, and three liberals (Breyer, Sotomayor and Kagan).
The possibility of the U.S. Supreme Court invalidating administration regulations and proposals, or striking down or misinterpreting legislation that the Biden Administration can cure with new legislation is great. But, some pro-Trump precedents it has recently adopted regarding executive authority, may inure to a President Biden's favor.
This state of affairs greatly limits Biden's ability to advance a progressive or liberal agenda during his first two years of office.
He can't realistically increase the size of the U.S. Supreme Court, grant statehood to the District of Columbia or Puerto Rico, pass a voting rights act restoration bill with teeth, or pass any other major legislation with any partisan bent.
He can use his allies in the House to leverage budget and appropriations legislation and can bargain with built in expiration dates of the provisions of Trump's signature 2017 tax law.
He can adopt new regulations and conduct foreign and military affairs with a fair amount of freedom. He also has considerable discretion in setting priorities for his executive branch departments.
He can make judicial and non-judicial appointments, although the Senate will likely try to block or delay his lifetime judicial appointments.
The Senate will have no incentive to abolish the legislative filibuster, because any legislation it passes can be vetoed by President Biden, or not agreed to by the Democratic Party controlled House anyway.
Biden's long service in Congress makes him well suited to try to negotiate bipartisan compromises and less partisan legislation.
Effectively, the situation puts Biden into a caretaker role.