Both his prime minister, Viktor Chernomydrin and retired General Alexander Lebed, his outspoken new security chief, said before yesterday's poll that they would like to see Russia under a coalition government after the president is inaugurated next month.
Although their remarks owe much to campaign tactics, there are plenty of signs that the issue was seriously discussed by members of the government and the Communist leader, Gennady Zyuganov, in the gap between the two rounds of the presidential election, in which both sides suddenly seemed to lower the tempo of their campaign drive. In recent days, Mr Zyuganov has repeatedly offered to set up a coalition government of "national trust", embracing a large slice of the existing administration.
For the president's part, the sharp slackening of pace can be explained by his mysterious illness, combined with the distracting hiatus caused by the arrival in the Kremlin of Mr Lebed, quickly followed by the firing of several of the most powerful and hawkish of the president's men.
So far, Mr Yeltsin has reacted negatively to talk of a coalition although this may be over a question of defining terms. Although he is committed to keeping the Communists from power, he may be willing to give Mr Zyuganov's group several socially orientated ministerial portfolios. So far the most the president has conceded is that he is willing to hold a "dialogue with all those for whom the fate of Russia is a top priority", including "honest communists".
But he may be keen to try to breach the gap in the country, which - as the election has made clear - is deeply divided. It may not be a question of "reds" and "whites', despite all the election rhetoric and ominous warnings of civil war. But a gulf exists between those who, though not enthusiastic about Mr Yeltsin, broadly favour reforms and others who want a restoration of at least some of the safety net of Soviet-style communism. It is a rift that Mr Yeltsin needs to heal, not least because of predictions that the country faces further serious economic hardships in the autumn.
So what happens next? The prime minister, Mr Chernomyrdin, whose political obituary has been written many times, seems likely to survive, having been impeccably loyal to his leader through thick and thin. He has weathered a poor performance as leader of of the government-backed party, Our Home Is Russia, in the parliamentary elections last December, and has so far shown little interest in challenging Mr Yeltsin's supremacy - a precondition for political survival in the Kremlin. It is he who would take over the leader's job if Mr Yeltsin dies in office, until another election is held.
Mr Lebed's future is less predictable. Last night's results suggest that a significant number of the 11 million voters won by the general in the first round (with the covert aid of the Kremlin) did migrate to Mr Yeltsin. It was with this in mind that the president made the former paratrooper the secretary of the Security Council and his national security adviser.
But it has taken less than a fortnight for his political naivity and clod-hopping manner to become embarrassingly obvious, at least to the outside world. After suggesting that he had stopped a coup on his second day in his new post, and then toning down his remarks, he caused further amazement by calling Mormons "scum" and calling for Western religious sects to be banned.
He was even at the centre of a minor election day flurry, when he accused a Spanish journalist of being a spy, and then retracted the remark. Popular he may be, but he is not invincible. Mr Yeltsin cannot run for election again, even if his frail health allowed it. Although he will probably keep the general for the time being, Mr Lebed's long-term survival is an open question - especially as he has already created a corps of enemies in the Russian military and the security services.
And Mr Zyuganov? If his defeat is confirmed, it is hard to see the Communists allowing him to be their presidential candidate again. Next time, they'll be looking for someone altogether more charismatic.