I realize it would have been a lot, but wars cost too and it would have preserved the Union... am I being an idiot?
It is difficult to answer questions like this because it is impossible for us to actually play out the counter-factual they demand we explore. In this case though, we can say with quite a lot of confidence that it is highly unlikely paying monetary compensation would have ever been a viable strategy for avoiding violent confrontation over slavery.
This was, to an extent, the policy of the British government in the Caribbean. When slavery is abolished in the British Caribbean in the 1830s, the colonial authorities recognised the enormous economic damage this stood to cause the economy of the region - over night, they were going to wipe out vast swathes of wealth and transition to a wage labour system with which the planter class had little experience. Furthermore, most of the islands were on track for a long-term labour shortage as a consequence of the abolition of first the slave trade and then slavery itself. Part of the British solution to this problem was to pay the slave owners of the Caribbean £20million (cumulatively, not each!) in compensation, divided up among those who could prove they had owned slaves, in accordance to how many slaves they had owned. To put that sum into perspective: that's about £2billion in modern terms, or 4% of the value of the entire British economy in 1830. That's a huge payout for the slave owning class in terms of the investment coming out of British pockets - it was a huge chunk of government expenditure in the year the money was set aside - but it's still only about £25 for each slave. Now, that's really not that much money at all per slave - and his was paid out unevenly, too, whereby some received much more than others.
In the US circa 1855, if I was a plantation owner looking to buy some extra slaves to work on my farm or plantation, I'm looking at a cost of about $800 per head on average - up to $1,000 or more for a prime field hand. If the United States had echoed the British policy of compensating slave owners for abolition, they would have been dramatically under-compensating the South in the eyes of its slave-owners. For reference, there are about 3.6million slaves in the United States in 1855; so for every slave owner in the South just to break even, you're looking at an expense of at least $2.88billion to cover the cost of emancipating every slave in the South, at a time when the total US economy was only worth an estimated $3.96billion by GDP (see Johnston and Williamson here). It would cost the entire United States nearly three-quarters of its annual economic worth to pay out compensation just for southern slaveholders to break even. Even if the US made double the investment in compensation that the British did as a share of their economy, you're looking at a tiny sum for each slave - nowhere near enough to make it worthwhile. In real life, of course, everyone selling off their slaves at once like that can't happen (and a mass sell off would decimate prices). But you get an idea of the sheer scale of wealth tied up in slaves.
You do find some contemporary abolitionists who moot the possibility of financial compensation for emancipation as a way of encouraging the end of slavery more gently; certainly by the 1850s though, southern slavery has created such massive wealth that it's simply impossible for compensation to be feasible if slave owners were going to receive the full value of their slaves. This is extremely significant because of the nature of slavery in the United States: a slave wasn't just a worker; he or she was a form of capital. Although a slave could and usually did depreciate in value with age (especially a female slave), they were also assets you could sell on whenever you needed to - and crucially, every time on of your slaves had children who also became your property and lived beyond infancy, your wealth increased because you had new slaves - who you paid nothing for - that you could sell at market. This is much less important in the British Caribbean, where slaves are generally used as mainly cheap labour and not really as a capital investment in the same way (at least by the 19th Century, except perhaps in Barbados).
Likewise, in the Caribbean, the compensation package was being paid by for chiefly by the full range of British taxation from across virtually the entire national economy; that is to say, the burden was shared by most of the British nation in some way. In the United States, you would have to raise this capital largely or exclusively from the Northern states - and make that politically justifiable to the electors living in them. It would be very difficult to justify abolishing slavery on any kind of moral ground whilst simultaneously collecting agonisingly large sums of money from non-slaveholders to pay compensation. Similarly, the British negotiated the abolition of slavery by creating a period of transition - a 'gradual emancipation' (which was how many Northern states abolished slavery in the 18th Century) - in which black people, though freed, were required to continue working for their former masters free of charge. In essence, the compensation was partially paid for by guaranteeing the slave owners a limited period of continued forced labour - and once that period gave way, the planters simply turned their attention to finding new ways of exploiting their ex-slaves or bringing in new labour (Indian workers, for example).
The South, for its part, was also enormously invested psychologically in slavery; slave holding and white supremacy had become an integral part of the culture of the southern elite. The Southern elite generally viewed freedom in terms of property rights rather than personal liberty as we might think of it today - to be free was to own property without limitation; to be unfree was to be property. For the wealthy white southern male, to own an estate with slaves was to be achieve a kind of social pinnacle; the ultimate form of masculine independence and self-determination. It was a cultural institution as well as an economic one, deeply embedded in the culture of the Southern elite. These were men and women who had defended slavery as a genuine moral good, as an institution that they believed (or at least, told themselves that they believed) actually uplifted everyone involved in it (including the slaves), not merely as an economic necessity.
It is, then, very difficult to imagine a realistic package of compensation to which Southern planters and slave-owners would have agreed with in substantial enough numbers to avoid the violent rupture of the Civil War. For the small slave-owner, and small-scale slave holding was the norm in the antebellum South, compensation below price paid was a significant threat to their wealth and livelihood and endangered their already often-precarious position in the social hierarchy. For large plantation owners, they risked not only their power base and huge sums of wealth in the abolition of slavery, but also saw a gross assault on their culture, their heritage, their identity, their way of life and their sense of personal honour. The economic and political infeasibility of full compensation, combined with the entrenched cultural resistance to abolition on the part of most powerful southern slave-owners, really precludes a strategy of mass compensation as a means of ending slavery in the antebellum South. Whilst some slave owners may have certainly found the idea agreeable (just as some saw mass 'colonisation' - the so-called 'return' of African Americans to Africa - as an acceptable alternative), it is difficult to imagine the kind of broad-based coalition you would need - in the North and South alike - ever forming in support around the mid-19th Century.
You're not an idiot, but your question is a bit off base: the onus of avoiding a war was not on Lincoln, who had just be elected president in a fair and free election performed as described in the Constitution. There was no action Lincoln took that caused the war, since the Deep South seceded before Lincoln took office. Rebel soldiers in South Carolina then fired on federal soldiers even while Congress was scrambling for a way to keep the South happy, even though they had just lost an election and begun an armed insurrection. Among the ideas being discussed was an unrepealable Constitutional amendment forever protecting slavery and declaring war on Spain in order to seize Cuba and give it to the South as a make-up present. Even with the Republican leadership trying to bend over backwards on everything but the expansion of slavery - the bedrock principle of the Republican Party - Southern troops opened fire before anything substantial could happen. If the insane concessions the government dangled in front of the Southern rebels weren't enough to slow them down, I think little else could.
No you're not being an idiot and indeed compensated emancipation was talked about at the time but you are missing two very key problems: the cost (/u/sowser covers that well) and the real problem: what happens to the black people? This later question was the real fatal flaw in antebellum slavery arguments because people didn't consider living side by side with former slaves to be a viable option which explained the immense (popularly forgotten outside of lincoln bashing) appeal of deportation to Africa. This is important in explaining especially the opinions of southern non elites.
Freehling has good stuff on this that i'll edit in when i get home in a few hours
Here's the problem: With the exception of the dedicated abolitionists, neither Lincoln nor the Republican party made it a policy to "free" the slaves to begin with. The premise of the question is wrong to begin with.
The platform of Lincoln and the Republicans was only to limit the spread of slavery in the territories. This had no bearing on existing slaves or slave owners in the "slave" states; hence no compensation was needed for slaves that were not going to be taken away or freed.
The problem - which was fully understood by the Confederates - is that the country was demographically turning against slavery. Lincoln won with 40% of the popular vote in a four-way race, and before that Kansas has voted to enter the Union as a free state.
Somewhere down the line, particularly given the rising tide of immigration from Europe (many of whom, like the Irish, were adamantly against slavery due to their own experiences), it was inevitable that 2/3rds of the country would be against slavery and therefore should have enough of a majority to force a change in the Constitution outlawing slavery.
The thing is this demographic transition was still going to take years. And while the Confederacy had lost control of the presidency, they still dominated the Supreme Court (which ruled in their favor in the Dredd Scott case), and had parity in the Senate (since Senators at this time were not yet elected and the South had engineered an equal number of slave and free states). Despite still possessing all of this power however, the South basically rage-quit from the Union which was only reflecting the increasingly anti-slavery sentiments of its population with the election of Lincoln.
Hence their acts of secession were in fact premature in the extreme. Lincoln did not plan to free the slaves in 1860, he only opposed its spread in the Territories. Lincoln could not have avoided the Civil war by paying the South money. He didn't even want to take away their slaves to begin with.
Moreover Lincoln's election merely symbolized the coming demographic changes that would result in slavery's extinction, but those demographic changes had yet to take effect. The South still held powerful positions in the Supreme Court and Senate to fight attempts to abolish slavery. But they didn't stay in the Union to argue their case or to ease the transition.
The South instead panicked because they realized that doom was coming thanks to their shrinking relevance and voting power in America as a whole, and decided to try and resolve the issue by war. In doing so they pretty much doomed the institution of slavery, because they never had a chance of winning the war based on the resources available. The entire war in fact only provided the pretext to abolish slavery altogether.
Edit: Grammar and additions.
Absolutely not. The issue at hand wasn't so much the institution of slavery itself being vital, many people at the time were beginning to realize that slavery wasn't economical. The real problem was that ownership of slaves was perceived as a measure of status in the antebellum South among the aristocratic elite. Abolition would have been a loss of status for those elites, something they were not willing to accept.
So basically, no, it wouldn't have made a difference. It would have possibly been more difficult to get the southern people to rally behind the idea of secession, since to them the government sold it as the North attempting to take away their rights illegally. However, it would not have made a difference to the outcome in any meaningful capacity.