Joe Biden wanted to raise taxes on wealthy estates. Mitch McConnell wanted to keep them low. The two longtime Washington politicians quickly discovered one point of agreement: the vote count.

With former president George W. Bush’s tax cuts headed toward expiration in December 2010, McConnell phoned Biden and told him that Senate Republicans had enough votes to keep the lower estate tax. Biden respected McConnell’s math. They eventually struck an agreement that marked the first of several times McConnell and Biden would reach a bipartisan deal to avert a looming financial cliff during the Obama administration, forming what multiple lawmakers and aides described as a sincere, if professional, bond that may soon be the most important in national politics.

“They genuinely like each other. There was a mutual understanding there. Even though he was the vice president, Biden’s mannerisms, his behavior — the cadence; the language — it was very senatorial,” said Rohit Kumar, who served as McConnell’s top aide during these negotiations, and is now co-leader at the national tax office of PwC, a consulting firm. “If I sensed that, McConnell sensed it, too.”

Senate Majority Leader Mitch McConnell (R-Ky.) on Nov. 9 threw his support behind President Trump’s legal challenges in the wake of his election loss. (Reuters)

President-elect Biden and Senate Majority Leader McConnell (R-Ky.), who’ve known each other for decades, have emerged from last week’s elections poised to become Washington’s new power brokers. Both have shown an inclination to make deals, and they have cut major deals working directly with each other. As Biden prepares to take office and lead a nation gripped by crisis and turmoil, the two men, both nearing 80, hold the potential to reach bipartisan agreements that can redefine the scope of government and shape the nation’s economy.

During his presidential acceptance speech on Saturday, Biden emphasized his belief in a “mandate given to us by the American people” to reach bipartisan agreements with congressional Republicans, who gained seats in the House and are set to retain control of the Senate under McConnell.

But the country and the two major political parties look very different from the last time Biden and McConnell served together in government, raising questions about whether new pressures will dash hopes of big bipartisan agreements. Biden risks a backlash from his base if he gives too much away to McConnell, whose policy priorities clash sharply with those of much of the Democratic base.

McConnell faces equally challenging political calculations. Biden’s defeat of Trump has hardened anger toward the president-elect on the right and reduced the appetite for cooperation among the conservative base. At the same time, Republicans will be defending a slew of Senate seats in purple states in 2022. McConnell, who has long been sensitive to the concerns of his members in seeking to retain his power, will be pressured to give them something to run on besides resisting the Democratic agenda.

The Kentucky Republican sent the clearest signal yet that he is sensitive to pressures from the right when on Monday he refused to recognize Biden’s victory and lent some support for Trump’s refusal to concede the race. “President Trump is 100 percent within his rights to look into allegations of irregularities and weigh his legal options,” McConnell said in a speech on the Senate floor. The remarks could complicate the abilities of Biden and McConnell to engage productively on legislative and personnel matters.

“I think the vice president will do his level best to find common ground,” said Phil Schiliro, who worked with both men as Obama’s legislative affairs director. “Whether they will get there is a separate question.”

Biden finds in McConnell a familiar negotiating partner from his time as President Obama’s chief emissary to Capitol Hill through years of high-stakes negotiations with congressional Republicans — who despised Obama — over the debt ceiling and possible government shutdowns.

Congress is younger and much more diverse than when both men entered it, Biden in 1973 and McConnell in 1985. Now, McConnell, 78, and Biden, 77, make an anachronistic couple to preside over Washington’s next chapter. With national politics increasingly polarized, the two men are considered careful coalition builders, seeking to represent the consensus views of their parties, at a time when most famous politicians are known for their ideological zeal.

Both sides have expressed cautious optimism that their partnership could produce significant breakthroughs, despite the gridlock and paralysis that have typically marred Washington during periods of divided government over the last two decades.

Obama had a famously frosty relationship with congressional Republican leaders, including McConnell and former House Speaker John A. Boehner (R-Ohio), who regarded him as condescending and professorial.

Trump and House Speaker Nancy Pelosi (D-Calif.) did not speak to one another for more than a full year following the impeachment inquiry, even as the nation was wracked by the coronavirus pandemic and a severe economic contraction.

Advisers to McConnell and Biden expect the two leaders to be in much more frequent contact, and, perhaps optimistically, get more done. Biden advisers expect the president-elect to work with the Senate Republican leader on bipartisan stimulus negotiations, although formal negotiations have not yet begun, according to multiple people who spoke on the condition of anonymity to frankly discuss private conversations. McConnell has publicly said a stimulus package should be Congress’ top priority after the election.

Those talks — which faltered for months between Trump and Pelosi — will now rest on a foundation built over the high-stakes negotiations between McConnell and Biden under the Obama administration. At a February 2011 event at the McConnell Center at the University of Louisville, Biden lavished praise on McConnell’s extensive knowledge of the Senate and thanked him for reaching “compromises that are necessary to what we both believe.”

On Saturday night, Biden repeatedly emphasized that he will seek to compromise with Republican lawmakers and is toying with appointing Republicans to his Cabinet.

“Refusal of Democrats and Republicans to cooperate with one another — it’s not some mysterious force beyond our control. It’s a decision, a choice we make,” Biden told supporters in Wilmington, Del. “And if we can decide not to cooperate, then we can decide to cooperate. And I believe that this is part of the mandate given to us from the American people. They want us to cooperate in their interest.”

McConnell has returned praise for the former vice president. In December 2016, McConnell gave a speech on the Senate floor over legislation dedicated to fighting cancer in honor of Beau Biden, the president-elect’s late son, while praising Biden’s “tremendous effort” on behalf of the bill. Last week, McConnell called Biden an “old friend” and publicly insisted on a peaceful transfer of power — even as Trump and many GOP officials ramped up their attacks on the integrity of the election.

“There is a reason ‘Get Joe on the phone’ is shorthand for ‘time to get serious’ in my office,” McConnell said in 2016.

For all their generational similarities, decades of overlap in government and penchant for negotiation, Biden and McConnell are different in many ways. McConnell cuts to the chase in public and private conversations, according to associates. Biden can be more loquacious.

“Biden is a much more expressive guy — that’s probably a subtle way to say it,” said Chuck Hagel, a former defense secretary under Obama who before that served in the Senate with Biden and McConnell. “Mitch is more reserved.”

The potential for bipartisan compromise will be challenged by immense pressure from their party bases wary of sacrificing key political and policy goals. Unless Democrats sweep a pair of Jan. 5 Senate runoffs in Georgia, a goal that some party leaders believe will be difficult, Biden will probably be left to deal with a Republican majority led by the man who said in 2010 that the GOP’s top priority should be to make Obama a “one-term president.” That prospect has alarmed liberal activists.

Left-leaning lawmakers say they are preparing to push Biden to approve a raft of executive orders on prescription drug prices, immigration and climate change, among other topics. At least one liberal Democratic senator has begun circulating a list of executive orders that Biden can sign without input from Congress, including crackdowns on monopolies and higher labor standards for government contractors, according to a draft of the memo reviewed by The Washington Post.

And while Biden’s penchant for dealmaking with Republicans has already rankled many in his own party and came under intense criticism from rivals during the Democratic presidential primary, opposition on the right is already mobilizing to respond to Biden. Liberal groups are also watching the process very closely.

“There is loyal opposition within the Democratic Party that is willing to make itself known, and there will not be the never-ending honeymoon that Obama had,” said David Segal, the co-founder of Demand Progress, a liberal advocacy group.