Breckinridge unlike Buchanan supported Douglas against Lincoln in 1858, despite Breckinridge's disagreements with Douglas over the Lecompton Constitution and the Freeport Doctrine. So it is just conceivable that the Democrats will be less violently divided and more open to a compromise candidate after four years of Breckinridge than under Buchanan. (Breckinridge was actually one of the more moderate leaders pf the pro-Southern wing of the Democrats. He had the support of the Rhetts and Yanceys but was not really one of them.)
Also, people forget that corruption in the Buchanan administration was one of the big issues of 1860--that's one reason why the Republicans called their candidate
Honest Old Abe. [1] If Breckinridge's administration is less corrupt than Buchanan's in OTL, the Republicans might have done marginally weaker in some close states. Of course that's a big "if"...
[1] "After the election, a Republican congressman noted that many “true men, from all parties, joined our standard because of the corruptions of the national administration.”619 Another Republican congressman assured Lincoln that “[n]othing did more to secure the enthusiasm and unanimity in your favor than the general impression and belief of the corruption of the present administration and the confident belief that your character and history afforded the best guarantee of a change for the better.”620 Agreeing was Republican Senator James W. Grimes, who said: “[o]ur triumph was achieved more because of Lincoln[’]s reputed honesty & the known corruptions of the Democrats, than because of the negro question.”621 Grimes’ colleague Lyman Trumbull shared that view, arguing that the “country has become disgusted with the profligacy, plunder & stealing here [in Washington] in the Departments. Mr. Lincoln owes his election in a great degree to a desire for a reform in these respects.”622 A leading Democrat, August Belmont, echoed those Republican leaders: “The country at large had become disgusted with the misrule of Mr. Buchanan, and the corruption which disgraced his Administration. The Democratic party was made answerable for his misdeeds, and a change was ardently desired by thousands of conservative men out of politics. This feeling was particularly strong in the rural districts, and did us infinite harm there.”623 " Michael Burlingame,
Lincoln: A Life https://www.knox.edu/documents/LincolnStudies/BurlingameVol1Chap16.pdf