There are several reasons Republicans, and most notably Lincoln, rejected compromise:
It included the extension of the MO compromise line to CA, something they steadfastly rejected (Free Soil, Free Labor, Free Men).
It would have forced Northern States to more rigidly enforce the fugitive slave law.
Most important, it would have dissolved the Republican Party. Lincoln would have been a one-term president and a man without a Party in four years.
It must be noted that Jefferson Davis and Robert Toombs as important members of the Committee of 13 supported the Compromise and only switched their votes to reject it when all Republicans on the Committee (5), at Lincoln’s insistence, voted against it.
Yes, it would kept all the other Southern States in the Union. Only SC was out at that point. Lincoln could have saved the Union had he wanted to do so in December 1860 by giving his support to the Compromise. This is why Lincoln’s rhetoric is hollow.