Heated discussions were held between the Kremlin's chief of staff, Valentin Yumashev, Mr Chernomyrdin himself, and parliamentary leaders over power- sharing proposals which would weaken Mr Yeltsin, and a Soviet-style economic plan.
Late yesterday, there were reports that a "broad consensus" had been struck. The lower house of parliament, the State Duma, has clamoured for more powers many times, but for once it has a real pressure point: its ability to confirm or reject Mr Chernomyrdin's nomination, due for debate on Monday.
The Kremlin is desperate for him to be installed in his post as soon as possible. Sensing weakness from the usually autocratic President, opposition groups - notably the dominant Communist Party - are threatening to reject Mr Chernomyrdin's nomination, dooming Russia to several weeks of ruinous political limbo. If the President wants his man, they argue, then he must pay the price - by giving up some of his powers and committing Russia to an economic plan which rolls back the so-called reforms.
Mr Yeltsin is not a leader who gives away power easily. His authority is, after all, vested in a constitution which he fought hard to get past the electorate nearly five years ago. And even if he signs away some of his powers, he is perfectly capable of reneging on the deal.
Yet power is what parliament is now demanding. And they just might get it. The documents were been drawn up by a tripartite commission, made up of representatives of both houses, the government, and a Kremlin observer. Last night drafts were placed before Mr Yumashev, at a meeting with Mr Chernomyrdin and the leaders of the parliamentary factions.
Before them were what amounted to draft proposals for a significant shift in the balance of power. The Russian constitution would be amended to give the Duma greater control over ministers and policy. The President would be banned from ruling by decree in on issues deemed within the cabinet and parliament's remit. He would be barred from proposing a candidate twice for prime minister, if the Duma rejected the nomination. Parliament would agree to debate what kind of guarantees to give Mr Yeltsin after the end of his term, and agree not to impeach him.
The initial reaction from the Kremlin was dismissive. The Yeltsin camp waved the plan away as biased. But it was willing to negotiate - perhaps in the hope of hoodwinking parliament by making promises to be broken later, but perhaps because Mr Yeltsin is genuinely ready to strike a bargain.
The Kremlin has, it was reported yesterday, produced its own much weaker political proposals. Chief among its conditions are an agreement that the Duma will not impeach Mr Yeltsin before the end of its term, next year. In return, Mr Yeltsin would agree not to dissolve it - as he can, if it refuses three times to endorse Mr Chernomyrdin's candidacy. Crucially, Mr Yeltsin is demanding a five-year moratorium on changes to the constitution.
Last night- doubtless to the horror of Washington, the G7, the European Union and the others begging him to stick to "reforms" - Mr Yeltsin appeared to have accepted the economic proposals, which include price controls, ending the rouble's convertibility, printing money and renationalisation.
It may be that the proposals will evaporate once Mr Chernomyrdin is behind his desk. But they may not. The old Gazprom chief is a luke-warm reformer. At his back stand committed interventionists such as Yuri Luzhkov, Moscow's mayor, and an army of anti-reform parliamentarians.
Western economists believe that the plan's implementation would be disastrous. "You would see empty shops, starvation," said Al Breach, a Moscow-based economic analyst.
Deciding what to do now will be painful for Mr Yeltsin. The mood is moving swiftly against him, at home and abroad. No matter how much back- slapping goes on between him and President Bill Clinton on next week's two-day Moscow summit, he has lost the faith of the West. Yesterday he dealt them another blow by going ahead with the sacking of his guru of market economics, Anatoly Chubais, who is beloved in the West, but loathed by Russians.
When Naina, Mr Yeltsin's long-suffering wife, told reporters yesterday she had an "intuition" that everything would be OK, it had the ghastly ring of the last muddled days of Nicholas 11 and his tragic family.