The U.S., Brazil, & the Security Council
The question why the US has been mildly supportive of Brazil as a new permanent member of the Security Council, despite its left-leaning government, is a good one. We can only speculate, of course. My speculation is along these lines.
It is not unlikely that the Security Council will be expanded. There is a lot of objection around the world to the effective control of the UN by the permanent members, which means primarily the US (since the UN fell out of complete control in the 60s, the US is far ahead in vetoes, its sidekick UK second, others far behind). And most of the world now considers the US a serious threat to peace, even their survival. Even the majority of the US population believes that the Security Council veto should be abandoned. These various pressures are likely to lead to diffusion of the power of the permanent members.
The two obvious candidates are Germany and Japan, the major industrial societies that are not already permanent members. But that would be problematic for Washington. A core element of US foreign policy since it became the world-dominant power during World War II has been to ensure that Europe and Japan-centered Asia not move in an independent path. Germany is Europe's powerhouse. The Franco-German alliance is the core of Europe's industrial, financial, commercial, technological,... strength. That's part of the reason for the hysteria about "old Europe" last year; it wasn't just passionate hatred of democracy, though that too was a factor, as the criterion for the old-new divide revealed. Northeast Asia, now comprising not only the Japanese economy but also South Korea and particularly China (closely linked to the Japanese economy), is the most dynamic economic region in the world, also holding about
half of global financial reserves and with potential access to vast resources, energy and others, in Siberia.
Preventing moves towards independence in the European and Asian political-economic entities has been and remains a central element in US foreign policy. That was a major factor in the Indochina wars. There was deep concern that an independent Vietnam might have a "virus" effect, "infecting" Southeast Asia with the curse of independence and finally leading Japan to "accommodate" to an independent Asia as its industrial heartland, meaning the US would have in effect lost the Pacific phase of World War II -- one reason why I think it is a serious analytic error to accept the familiar conclusion that the US lost the Vietnam war; it achieved its major war aims by destroying Indochina, and though it didn't achieve its maximal aims, that's hardly "defeat," as the business world understood 30 years ago. The same concerns were also a factor in the reconstruction of Europe on the basis of military aid and integration (far more significant than the Marshall Plan) and many other policies. They were surely a key feature in invading Iraq, which, as Zbigniew Brzezinski recently put it, provides the US with "critical leverage" over European and Asian economies. He is reiterating a point made by top planner George Kennan half a century earlier, when he observed that control of Middle East oil gives the US "veto power" over what Japan might do some day if it recovers from wartime disaster. Control over energy has always been a leading factor in world domination, a fact often ignored in discussion of access to oil. Reliance on Middle East oil is a lesser factor, so I think the record shows (and simply analysis of global strategy and the nature of oil markets).
Coming back to Brazil, I think there are good reasons why the US would want to block the natural expansion of the Security Council to its serious rivals, Germany (linked to France) and Japan (linked to China). Whatever its government, Brazil is far more dependent on US will, sometimes exerted through the IMF. Recent years reveal that quite dramatically; left-oriented or not, the government has effectively pursued the policies dictated by the international financial community and the US. Brazil also has ambitions and potential to lead an independent bloc of nations, but those would be nations of the South, much less threatening to US world domination, whoever happens to be in the government.
If we assume rational planning, with the usual cynicism that guides it, these seem to me reasonable speculations. Only speculations, of course. We don't have documentary evidence and there is very little investigation and reporting about such matters, which simply cut too deep to be acceptable, even thinkable.