Melodramatic they may have seemed, but there was a clear political purpose behind Mr Yeltsin's bold words and even bolder deeds. When he sits down in Helsinki on Thursday for a day of talks with Bill Clinton - whose health, ironically enough, is in the headlines following a ripped tendon - he wants the US president to be in no doubt that, from now until the end of his term of office in 2000, he will stop at nothing to ensure that he leaves Russia as a powerful, orderly, energetic, reforming democracy.
Officially, the Helsinki summit has a three-part agenda covering European security, arms control (including intercontinental nuclear weapons) and improving Russia's economy. Unofficially, the question hanging over the summit is whether the US determination to expand Nato into eastern Europe could prove so harmful as to torpedo Mr Yeltsin's last and bravest effort at ensuring the irreversibility of Russia's post-communist political and economic reforms.
As the 66-year-old Kremlin leader knows, the stakes for Russia could hardly be higher. The reform process has virtually ground to a halt since Mr Yeltsin's re-election last July, with crime and corruption rampant and more than half the population affected by delays in the payment of wages and pensions.
"Most of the people of Russia are unhappy with the present and fear the future," he said in his annual address to parliament. "Every reserve of human patience has been exhausted. We have no time for procrastination or political manoeuvres."
Hence his extraordinary announcement last Tuesday that he was dismissing the entire government except the Prime Minister, Viktor Chernomyrdin, and the latter's newly appointed deputy, Anatoly Chubais. It was an unmistakable signal to Russians, and to Mr Clinton, that there will be no more fudge, drift or shilly- shally in government policy.
Mr Chubais is the reformer par excellence: not just the architect of Russia's industrial privatisation programme (the largest in history) but a talented administrator who effectively ran the Kremlin during Mr Yeltsin's absence last year with heart trouble. Though unpopular with millions of ordinary Russians, Mr Chubais knows how to look after himself in the treacherous environment of Kremlin intrigue - he orchestrated the ex-general Alexander Lebed's fall from grace last October - and Mr Yeltsin is counting on him to shake the government and bureaucracy out of their torpid ways.
Yet it would be misleading to suggest that Messrs Yeltsin, Chernomyrdin and Chubais are about to embark on a frenetic binge of radical, Westernising reforms to the economy of a kind last seen in the early months of 1992. In his speech to parliament on 7 March, it was significant that the president stressed that order, as much as reform, would be the key theme of the last three years of his administration.
"Order" is a word that gladdens the hearts of many Russians, with their historical memories of epic periods of anarchy such as the Time of Troubles of the early 17th century and the Revolution and Civil War of 1917-21. In post-communist Russia, one of the most common complaints of the populace is that there is too much disorder: mafia killings, bombs on public transport, robberies, business trickery, corruption in government and - for pensioners, doctors, teachers and servicemen - no income for months on end.
Yet all Mr Yeltsin's best-laid plans for a large dose of order and reform at home could come to nothing if he and Mr Clinton fail to strike a deal over Nato's planned expansion, by far the biggest problem in US-Russian relations. Without a compromise that Mr Yeltsin can defend as being in Russia's national interests, he will quickly become vulnerable to attack from his domestic opponents, including the nationalist and communist majority in parliament, and the still ambitious Mr Lebed.
They would like nothing better than to drive Mr Chubais out of office, and it would not bother them if they paralysed Mr Yeltsin's presidency in the process. Fortunately, there is just a chance Mr Clinton and Mr Yeltsin will reach a deal of sorts in Helsinki.
In return for Nato's expansion to include the Czech Republic, Hungary and Poland, Russia and the Atlantic alliance hope to agree later this year on a "charter" defining their relations. It would provide for joint operations in such fields as peacekeeping, nuclear proliferation and counter-terrorism, and it would give Russian military officials access to Nato intelligence, field exercises and command centres.
Mr Yeltsin initially insisted that the charter should be legally binding. At Helsinki, however, he may accept a less rigid formulation ("politically binding"), so long as the charter is approved by parliaments in all Nato's member states. One sticking-point may be Mr Yeltsin's demand, voiced last week, for Nato to rule out the admission of any former Soviet republics, including the three Baltic states. It would appear politically impossible for Mr Clinton to make such a concession in public.
Mr Yeltsin predicted last Friday that the summit would be "the hardest in all the history of Russian-American relations". That is because, perhaps for the first time since the summits between Ronald Reagan and Mikhail Gorbachev in the Eighties, there is real bargaining to be done. For Mr Yeltsin, though, one thing is clear. To ensure his place in history as a great reformer is not badly tarnished over the next three years, he desperately needs the summit in Finland to be a success.