By and large, the Monroe Doctrine was viewed favorably by the American people and their representatives, and was seen as an integral part of their dealings with foreign nations. As early as 1824, the General Assembly of Pennsylvania passed a resolution declaring the accordance of this new Doctrine with the country's republican virtues, and the necessity of protecting the newer republics in the Western Hemisphere from European meddling.
It appears that by 1849 there were some who believed that the Monroe Doctrine was not a timeless directive for American foreign policy, but that it was only relavent at the time when Monroe put it forward, and argued that the nation should adopt a more isolationist stance. This is what the North American Gazette and United States Gazette are arguing against, and accuse the Washington Union, which ran a story in which they advocated for isolationism as a way to avoid "entangling alliances" of having foreign sympathies and of supporting the interests of foreign nations over American interests.
In 1895, The Daily Inter Ocean of Chicago, asked every Congressman what they understood of the Monroe Doctrine to mean and if they supported enforcing it through war if necessary. The answers all share similar views, that America should not tolerate European countries attempting to exercise influence over any country in the New World, and it is the duty of America to stop any European interference by war if necessary. The similarity of all of these men's statements reflects that this was the position that their contituencies would have expected them to take, and that the Monroe Doctrine was clearly regarded highly throughout the country.
In the 1890's, a territorial dispute between Venezuela and the United Kingdom became a test of what exactly the United States meant when it claimed that it would take any act of foreign intervention in the New World as an act of agression towards America. This was the context in which every congressman was asked what he took America's duties under the Monroe Doctrine to be. What America's response amounted to was that any controversy involving countries in the Western Hemisphere affected American interests and thus fell under the American purview, and in the end of the dispute, the United Kingdom conceded and allowed america to act as arbiter in the dispute, tacitly conceding to the ameican interpretation of the Monroe Doctrine.
The Monroe Doctrine was recieved in a number of ways after its conception in 1823. Some countries reacted with gratitude and acceptance, some with anger and denial, while others (namely major European powers) chose to ignore the policy all together, viewing it as nonessential. It was around the end of the 19th century, after the Britain/Venezualan conflict, when the world began viewing the Monroe Doctrine as a legitimate foreign policy tool to be respected. Citizens of the U.S. could now rally behind their flag knowing, with certainty, that the U.S. was a major power in the western hemisphere and around the globe. There were still some countries in South America and in Europe that were hesitant to accept the Monroe Doctrine as a policy all must adhere to, but U.S. would, over time, strengthen their position as a major player in the global scheme of things, using many tools, including the Monroe Doctrine.
Although a majority of U.S. citizens believed that the Monroe Doctrine should be interpreted at face value, with the United States as the leading power in the western hemisphere, there were those with opposing views. Many people felt that the United States should head the warnings put forth in the Farewell Address of George Washington and remain an isolationist nation. Some believed that the Monroe Doctrine should still be apart of U.S. foreign policy but that it should evolve with the changing times. There were certainly other interpretations involving the Monroe Doctrine but these three variations appear to be the most common.