If their increasingly vocal and influential campaign comes too late to prevent Nato issuing invitations to join at the Madrid summit in July, it could still prevent one or more of the sixteen Nato member states ratifying the accession of new members in April 1999. That would be enough to prevent enlargement taking place as planned.
The opponents of enlargement include academics, journalists and former defence and security chiefs, many of whom were involved in the Cold War, the arms reduction negotiations in the late Eighties, and in the talks on the unification of Germany. The growing band of opponents, who do not necessarily oppose enlargement, but believe it is being rushed, includes Robert McNamara, secretary of defense from 1961-68; and Paul Nitze, former deputy defense secretary and US delegate to the Strategic Arms Limitation Talks (Salt) from 1969 to 1974. George Kennan, a former diplomat, academic and elder statesman, has said that Nato enlargement would be the gravest error in foreign policy towards Russia since the Second World War.
Although no written undertaking was given that German unification within Nato would not be accompanied by a further eastward expansion of the alliance, a number of those involved maintain that the Soviet Union - to which Russia is heir - was given that impression.
US government policy, stated by President Bill Clinton and Secretary of State Madeleine Albright, is for an early enlargement which will probably include Poland, Hungary and the Czech Republic in the first wave. Opponents say that policy was driven by US politics, to appeal to voters of central European ancestry in the key mid-western constituencies.
Britain has, as usual, followed the American line. The "mission statement" given on Monday by the Foreign Secretary, Robin Cook, committed Britain to "an enlarged Nato".
Bevis Longstreth, a Law Professor at Columbia University and President of the Winston Foundation for World Peace, visiting London this week, said there were powerful arguments against hurried enlargement which could sway western parliaments. He stressed the cost to present Nato states and to the applicants; money which would be better spent improving their economies, and the risk of offending and isolating Russia, which could have catastrophic long-term consequences, with nothing to show for it.
The most obvious argument for delaying enlargement was the cost: an estimated $40bn (pounds 25bn) for European Nato members and $100bn for the US, plus the cost to new members to upgrade forces to Nato standards in certain areas or to make them compatible with Nato.
"It's preposterous for them to be spending money on the military", Professor Longstreth said. "It's throwing them an expensive bone, rather than admitting them to the EU." He added that many people doubted whether expanding to the east was the highest priority, as the security threats Nato was best suited to dealing with lay to the south.
The biggest danger, however, was isolating Russia in what threatened to become a re-run of Germany's isolation after the Versailles Treaty of 1919 imposed humiliating and crippling war reparations. Isolating Russia could give rise to nationalism and, possibly, the appearance of a dangerous dictator.
The planned Nato-Russia "Charter", or "Act" as it will probably be known, is designed to prevent this, by involving Russia in Nato business. However, the US policy has resolutely opposed giving Russia any "veto" over Nato decisions.
As the Madrid summit approaches, a significant body of opinion is being mobilised in the US and Europe at least to delay enlargement. "We don't have to defeat it", said the professor. "We just have to say 'hey, let's wait'."