If by "going their own way" you mean 'to expand slavery into the new territories' then you'd be right. That was the build up to the Civil War.
Lincoln considered the southern states as "loyal states that were "subverted" by traitors.".....
"...Whereas, a rebellion now exists whereby the loyal state governments of several states have for a long time been subverted, and many persons have committed, and are now guilty of, treason against the United States; and.....<snip>
"...And still further, that this proclamation is intended to present the people of the states wherein the national authority has been suspended, and loyal state governments have been subverted, a mode in and by which the national authority and loyal state governments may be reëstablished within said states, or in any of them; and while the mode presented is the best the Executive can suggest, with his present impressions, it must not be understood that no other possible mode would be acceptable....."
Neither Lincoln or the US government recognized the South's "so-called confederate government" and they always referred to it as a 'rebellion' or 'treason' but never a war. They were very careful not give the South's "so called secession" any legitimacy......
"....And I do further proclaim, declare, and make known that whenever, in any of the States of Arkansas, Texas, Louisiana, Mississippi, Tennessee, Alabama, Georgia, Florida, South Carolina, and North Carolina, a number of persons, not less than one tenth in number of the votes cast in such state at the presidential election of the year of our Lord one thousand eight hundred and sixty, each having taken the oath aforesaid, and not having since violated it, and being a qualified voter by the election law of
the state existing immediately before the so-called act of secession, and excluding all others,
shall reestablish a state government which shall be republican, and in nowise contravening said oath, such shall be recognized as the true government of the state, and the state shall receive thereunder the benefits of the constitutional provision which declares that “the United States shall guaranty to every state in this Union a republican form of government, and shall protect each of them against invasion; and on application of the legislature, or the executive, (when the legislature cannot be convened,) against domestic violence......”
Proclamation of Amnesty and Reconstruction, December 8, 1863
The federal government won the war that rendered the South's seccession as null and void.