No, it isn't. See below.
... but if somehow the unionists kept the South from seceding (maybe South Carolina starts an abortive attempt but ultimately fails to bring the other states in)...
South Carolina secessionists were divided between an immediatist faction and a cooperationist faction. The latter group wanted to wait until action could be coordinated among all the Southern states, presumably by a multi-state convention. They argued that it could be disastrous for South Carolina to act unilaterally.
Also, IIRC, the cooperationists wanted to delay action until Lincoln had taken office and Done Something to push all the slave states to secession with overwhelming support.
In late 1860, there was a ceremony for the completion of a new railroad linking South Carolina and Georgia. Many prominent men from both states were present, and the secession issue was discussed. At this meeting, many of the Georgians present assured the South Carolinians that Georgia was sure to declare secession as well. This was a significant boost to the immediatist faction, which carried the day at the South Carolina convention a few weeks later.
Suppose that ceremony had not been held, or due to bad weather was not well-attended; and unsure about the attitude of Georgia, the South Carolina convention adopted the cooperationist plan. This is copied in the rest of the Deep South, the Upper South, Missouri, and Kentucky. All these states send delegates to a convention which assembles in Richmond in late February 1861.
Meanwhile, Southern members don't withdraw from Congress, which does not admit Kansas or pass the Morrill Tariff.
Lincoln is inaugurated in on 3 March. Aware that fearful Southerners are watching his every move, and that the Fire-Eaters will seize on any misstep to incite pro-secession panic, he acts with great caution. His first area of action is appointment of Federal officeholders. Lincoln OTL sought to include a Virginian in his initial cabinet, in hopes of averting secession. He's almost certain to attempt something similar ITTL. He must appoint Southern residents to Federal posts in the South. which is going to be tricky. Many Southerners would refuse any appointment by the hated Republican - but the offices must be filled, and Lincoln would go to great lengths to find acceptable men.
As it became clear that Lincoln was
not using the Presidency to subvert slavery in the South, enthusiasm for secession would wane. There would be nothing for the Fire-Eaters to point to as an outrage justifying secession. The Southern convention would adjourn after three months or so.
what sort of policies would Lincoln enact?
There are two parts to this question. What policies would Lincoln advocate? And what policies could he get Congress to enact? Bear in mind that Republicans lost 8 House seats in 1860.
His main political goals at that time were:
- Admitting Kansas as a free state.
- Enacting a protective tariff.
- Initiating a transcontinental railroad.
When Congress meets in December 1861... I think he gets Kansas. But the tariff, no, or only in compromise form. The railroad may also have to be compromised.
Foreign policy may become an issue by that time, with the French presence in Mexico raising American hackles. If Lincoln manages that well, even Southerners will applaud.
Would he get a second term?
Would he want one? No Whig ever ran for a second term, and Lincoln was an ex-Whig.