To some degree, the Constitution did represent an accommodation of both liberal and conservative visions of republicanism.
On the conservative side, the Constitution did try to shield the government from excessive input on the part of the people. (Please note that this is not something that conservatives today would want. This is one aspect of conservatism as it was seen at the time of the writing of the Constitution.) Conservatives were less likely to believe in democracy and were more likely to believe that something similar to a monarchy was needed. They felt that the people were not really capable of governing themselves and that some sort of paternalism on the part of the elites was needed. For this reason, for example, the Senate was not to be directly elected and neither was the President or the Supreme Court.
On the liberal side, the Constitution did give some power to all the people and it did work to protect rights. The Constitution did give the people the ability to directly elect members of the House of Representatives. The Constitution also did away with things like established churches which were typically admired by conservatives. In these ways, the Constitution also accommodated the views of liberals.