"Of course Brazil, China, INdia and Russia could defeat USA, UK and Canada. They're some of the biggest countries around with some of the highest populations."

I think judging the outcome of such a war requires a little more sophistication than simply adding up population counts. Even adding up each side's number of soldiers, tanks, airplanes, etc. doesn't even begin to do the matter justice.

The whole question asked in the title of this debate is much too vague to be able to answer it with a simple yes or no, because victory depends on what either side would actually hope to achieve in a war. If the question was "Could Russia and her allies force the U.S. to surrender in a conventional, non-nuclear conflict?" then the answer to that would have to be a flat-out NO, no chance in hell. On the other hand, if the question was "Could Russia defeat an American attempt to invade and conquer Russia?" then the answer to that would be, hell yes, it could!

The U.S. is the only nation on the planet that not only has a very powerful military but also has the ability to project a substantial share of that power to almost any point on the globe. Its navy, by virtue of technological prowess, operational experience and sheer size, is second to none. Other navies may match or even outperform the U.S. Navy in certain aspects (for instance, some believe the Brits have the best submarine force in the world), but none of them could hope to take on and defeat the U.S. Navy to the point where they would achieve naval superiority (let alone supremacy) in the American hemisphere. Without naval supremacy, an invasion of the U.S. becomes outright impossible. Even if the Chinese army were 100 times as large as the American one, as long as America dominates the seas, none of that matters.

Now China (and Russia) may very well already have the ability to keep the U.S. Navy at a respectful distance from its own shores ... both have growing numbers of very capable, modern aircraft with anti-ship missiles as well as large numbers of modern, land-based anti-ship missiles. They also have a relatively small (but growing) number of capable frigates / destroyers / cruisers and submarines which, while probably outgunned in a blue-water confrontation against the U.S. Navy's carrier battle groups, can pose a serious threat to American forces that come too close to Chinese / Russian home waters.

Both China and Russia also have quite large, reasonably well-trained and equipped armies well-able to defend their homeland from the well-trained and equipped but not-that-large-anymore U.S. Army / U.S. Marine Corps. Again though, while these armies are very fearsome opponents in a regional conflict, neither have the ability to project their power very far from home let alone the Americas.