In the next two and half months, Joe Biden needs to build a governing team to help him tackle a historic pandemic and rebuild the economy – all while winning approval from what is likely to be a Republican-controlled Senate and holding together an unruly coalition of Democrats.

It's a task that will be nearly impossible to pull off.

The Biden transition team has been vetting potential candidates for months and will present the president-elect with potential choices in the coming days. Biden is expected to focus first on posts involving public health and the economy, including the secretaries of the Treasury and Health and Human Services, along with West Wing personnel. The former vice-president intends to be deliberative and is not likely to announce cabinet nominations in the first week, according to an official close to the Biden team.

The president-elect will face incoming on several fronts, including from Democrats who expect him to nominate the most diverse Cabinet in history. That goal is not always compatible with the push from the party's vocal left wing to nominate the most progressive Cabinet since Franklin D Roosevelt.

The Wall Street and Silicon Valley interests that poured money into Biden's campaign over the final stretch have a different set of priorities. So do Senate Republicans, at least a handful of whom Biden will need to confirm his nominees, if, as seems likely, the Republican Party maintains control of the chamber.

Biden can make history by nominating a person of colour or a woman to head the Treasury or Defence departments – the only two remaining departments that have only ever had white men lead them.

Michele Flournoy, a former under secretary of defence for policy, is already the front runner to lead the Pentagon. A number of women and people of colour are also in the mix for the top job at treasury, including Federal Reserve Governor Lael Brainard and Teachers Insurance and Annuity Association of America (TIAA) chief executive Roger Ferguson.

Biden, who pledged to unite the country during the campaign, is likely to try to keep his coalition together by nominating a mix of progressives, moderates and even a few Republicans. He is also likely to draw in some fresh faces alongside long-time Biden loyalists. “I think one thing Joe Biden has always liked is a variety of viewpoints,” said former Senator Mark Pryor, who served for six years alongside Biden in the Senate. In other words, expect Biden’s own self-styled “Team of Rivals.”

The likelihood that Kentucky Republican Mitch McConnell will remain Senate majority leader, however, means that every Biden nominee will need to win at least a few Republican votes. That will limit Biden’s choices and makes it less likely some left-wing choices would be confirmed. House Democrats are also more wary of Biden tapping any of their members from competitive districts, given that their majority just narrowed and they do not want to risk any upset special elections.