In 1850, the District had 51,687 people. https://en.wikipedia.org/wiki/Demographics_of_Washington,_D.C. That's more people than Nevada had when it was admitted to the Union. https://en.wikipedia.org/wiki/Nevada Southerners are worried that the admission of California will destroy the sectional balance? Counteract it with the new State of Columbia (or even Washington--after all, Washington Territory in the far Northwest had not yet been created, so the name is still available...). True, the Constitution seems to require a federal district under direct congressional jurisdiction; but this could just consist of a tiny area containing a few essential federal buildings, with the rest of the old District becoming a state...
(In 1860, preventing the new state from seceding is obviously going to be a priority for Lincoln, assuming his election isn't butterflied away.)