In the statement "A house divided against itself cannot stand," Abraham Lincoln, the 1858 Republican candidate from Illinois running for the U.S. Senate, was referring to the idea that the United States could not continue half-slave and half-free. This meant that the country could not sustain a situation where some states allowed slavery while others did not. Lincoln believed that this division would ultimately lead to conflict and the downfall of the nation. He was emphasizing the need for unity and the importance of addressing the issue of slavery to prevent the country from collapsing due to internal divisions.