Jackson being a southerner and a slaveowner of the landed plantation class would have tried to work a deal but in the end like many others of 1860-61 would have said screw it and sided with the secessionists.
I wouldn't take this as a given. Jackson had very harsh words for Calhoun, purportedly: "John Calhoun, if you secede from my nation, I will secede your head from the rest of your body." Jackson was in many ways a prototypical Southern Unionist, and many pro-Union Southern Democrats called themselves "Jackson Democrats" during the Civil War era. Tennessee was also the Confederate state with the most Unionists. Genuine Jacksonians were a bit of a dying breed by the Civil War, but one obvious and famous one, Andrew Johnson, was himself a Tennessee Unionist.