Peter Meyer at the Congressional Research Service wrote a report on the Organization of American States that neatly sums up the paradox of U.S. policy in Latin America.
On the one hand:
The relative decline of U.S. influence in the Western Hemisphere has manifested itself within the OAS on a number of high profile decisions in recent years, including a 2009 decision to repeal the 1962 resolution that had suspended Cuba from participating in the organization.
And on the other:
Even as some Members of Congress assert that the organization acts against U.S. interests, a number of policymakers in the broader region argue that the OAS imposes U.S. policies. Given these views, some analysts maintain that “any reform to the OAS that begins in Washington, especially in the U.S. Congress, can have the potential to backfire” and provoke opposition in the hemisphere.
In other words, there are constant calls for the United States to exert its influence more (just yesterday, the WSJ asked the Obama Administration to be more aggressive with Venezuela, albeit without any specifics) but sometimes exerting more influence leads to less influence because there is backlash. To the extent that the US has become less influential in the OAS (which I could quibble with) it is in large part because in the past the US tried to be too influential.
The trick is finding the sweet spot without doing something stupid.