From the 1872 election:
Due to Grant's tainted first term, several Republicans called for the creation of a new third party. This new party formed in 1870 in Missouri and called itself the Liberal Republican Party. The name was selected to suggest three things: its members were republicans, they were moderate republicans and not radical republicans, and they were a liberal reform faction of the party ready to fight corruption at the highest levels. The Liberal Republicans held their convention in May 1872 and nominated Horace Greeley to run against Grant for President.
The platform of the Republicans was possible civil service reform and a pledge to continue to support civil rights in all sections of the nation. They condemned racial and religious discrimination and called for granting women greater rights. The Liberal Republicans endorsed ending radical Reconstruction and pulling federal troops out of the South. Democrats had trouble electing a nominee and realized that they likely would not be able to win, even against a split Republican Party, and therefore decided to support Greeley.
Greeley's campaign was primarily the theme of "more honest government." He campaigned for an end of radical reconstruction.
There were more attempts at character assassination than at debating the issues. Greeley's camp attacked Grant's corrupt administration, and Grant's camp attacked Greeley for his support of spiritualism and vegetarianism.