``I think that the Russian government understands exactly what NATO enlargement is going to mean as far as the stability for the future,'' Cohen said yesterday as the Senate began a push toward a final vote on the measure to add Poland, Hungary and the Czech republic to the 49-year-old military alliance.

Criticism ranges from fear of the effect it would have on US-Russian relations to concern over the cost to American taxpayers.

But as Cohen, a former Republican senator from Maine, made the rounds on Capitol Hill lobbying ex-colleagues, leaders of both parties predicted NATO expansion would finally win approval and by a decisive margin.

A close vote was expected on a proposed amendment by Republican Senator John Warner and Democratic Senator Daniel Patrick Moynihan for a three-year moratorium onfurther expansions.``It is the right thing to do for our country and for peace and security in Europe,'' said Senate majority leader Trent Lot of the overall measure.``I think it's the natural extension of the end of the Cold War. And it's enlargement of the ring of freedom in Europe.''

Lott pledged to keep the Senate working without distraction until a final vote, which he suggested could come by tomorrow. Senate Democratic leader Tom Daschle of South Dakota, who brought Cohen with him to his regular morning news conference, said rejection of the treaty modification could send a tragic and an extraordinarily damaging message to the European Community and the rest of the world about how the United States views its role.''

But opponents a diverse and bipartisan group took their complaints to the Senate floor, calling enlargement too costly to US taxpayers and an unnecessary poke-in-the-eye to Russia.