For example, wouldn't some Republican politicians think that a Union without the South would significantly shift the national Overton window in their direction?
During the Secession Crisis between December 1860 and April 1861, there were voices on both sides calling for "peaceable separation", "peaceable dissolution," and "peaceable disunion". One of the most powerful Northern voices on this matter was Horace Greeley, publisher and editor of the most widely read newspaper of the era, the New York Tribune. He was a longtime abolitionist and a founder of the Republican Party. When Lincoln's election had become apparent, Greeley wrote in a November 9, 1860, editorial under the headline "Going To Go":
"The telegraph informs us that most of the Cotton States are meditating a withdrawal from the Union because of Lincoln's election...We have a chronic, invincible disbelief in Disunion as a remedy for either Northern or Southern grievance...[S]till, we say, if anybody sees fit to meditate Disunion, let them do so unmolested...[I]f the Cotton States shall become satisfied that they can do better out of the Union than in it, we insist on letting them go in peace."
This would later be rephrased as "Let the erring sisters go in peace" or "Let the wayward sisters depart in peace", though the phrase doesn't actually appear in the editorial. Greeley's New York Tribune would write similar sentiments for most of the Secession Winter.
Many other Northerners took similar positions during the Secession Winter. Lincoln's soon-to-be Secretary of War, Edwin Stanton, was reported to have said, "Oh, I would let the South go; they will be clamoring to get back in three years."
Future President Rutherford B. Hayes, then the outgoing Solicitor for the city of Cincinnati, and soon to be Union Army volunteer once the war broke out, wrote in his diary on January 4, 1861:
"The free States alone, if we must go alone, will make a glorious nation. Twenty millions...stretching from the Atlantic to the Pacific, full of vigor, industry, inventive genius, educated, and moral; increasing by immigration rapidly, and, above all, free—all free—will form a confederacy of twenty States scarcely inferior in real power to the unfortunate Union of thirty-three States which we had on the first of November. I do not even feel gloomy when I look forward. The reality is less frightful than the apprehension which we have all had these many years."
In California, the state congressmen aligned with Breckinridge's Southern Democrats were led by Charles Lindley, who declared during the Crisis:
"Let us have union if we can; peaceable dissolution if we must but conflict never."
But Lindley's speech pointed out the problems with "peaceable dissolution," because in the very next line he said, if the Union should be dissolved, why should California stay with the free states? He doesn't advocate that they should join the Confederates, either, but instead, California should establish a "Pacific nationality" all its own, as an independent country.
The issue facing everyone was what a "peaceable separation" would even entail. Greeley's stance in favor of it was only because it was preferable to compromise over Northern and Republican principles. U.S. Senator Benjamin Wade of Ohio echoed this sentiment when he wrote:
"The day of Compromises has past, and that Government which is moved to temporize by the threats of Traitors is not worth preserving."
The Southern political class wasn't really looking for "peaceable separation" as a first resort, either, as Lindley's speech makes clear. They wanted "compromise" that would entail the North recognizing the South's right to remain slave states forever and always and deny the North any constitutional ability to interfere with it, ever, which is what the "Corwin Amendment" to the Constitution attempted to do. They also wanted the North to cede some amount of Western land to become slave states, and any kind of "free soil" future for the West was a non-starter. The Republican Party refused to negotiate on such terms on either issue. So a "peaceable separation" really wasn't any more attainable than a compromise that kept the Confederate states within the Union, because those issues had to be resolved whether they stayed within the Union or not. As Constitutional scholar Nathan Dane had written thirty years earlier:
"If there shall ever be a separation...the immense property of the United States will be a bone of contention and with other causes, will in time bring on hot contention or war, or prove a separation far worse than compromise...Secession, not assented to, draws the sword."
In addition, as author Charles Adams points out in his book When in the Course of Human Events: Arguing the Case for Southern Secession, a "peaceable separation" did not resolve outstanding tariff issues the two sides had, and was likely to lead to a trade war, with each side's ports trying to undercut the other in importing foreign goods. This was yet another issue that would need to be resolved to avoid an immediate or eventual war, to make "peaceable separation" possible.
And that's to say nothing of the effect on the legitimacy of the rule of law under the U.S. Constitution. If the South were allowed to go, there would be little to stop the remaining states to pull the same stunt during the next political battle. An editorial from February 4, 1861, first printed in the Cincinnati Times sarcastically painted "peaceable separation" as just such a failure to defend the Constitution:
"[Disunion-supporting Republicans] have created the whirlwind and now flee from the storm. They have battled for national supremacy, and dare not seize the power they have won. They prefer, it seems, to rule over half the nation, than to defend the whole."
In other words, it wasn't enough to just say, "Hey, let's go our separate ways." Division of U.S. property within the Southern states, division of U.S. property out West, the division of national debts, treaties over the recovery of escaped slaves, treaties over control of the Mississippi River that interior Northern states depended on for commerce, treaties over international trade and tariffs, and so on and so on...These were all issues that a "peaceable separation" couldn't address any better than a compromise keeping the South part of the United States could.
In the few months between the time secession began and the time Fort Sumter was attacked, the Republican Party's majority position, then, was to not compromise on the South's terms in regards to slavery's Western expansion, fugitive slave laws, and more, while the South's majority position was to not allow any of these Republican positions be allowed to stand.
South Carolina opened fire on Fort Sumter, and pretty much immediately, most "moderates" were pushed one way or the other, as this May 1861 editorial from the Boston Daily Advertiser makes clear. Greeley and people like him dropped calls for "peaceable separation" and began calling for the U.S. to stand united against a movement that would destroy the Union entirely. Southerners who had called for "peaceable separation" now wanted to win that separation through war, so they could force the North to assent to all the positions on slave law that concerned the South.
Politicians in the North who continued to advocate "peaceable dissolution" very quickly found themselves in the minority. The more powerful voices in the North opposing the war did it more on the terms of "Let the South back into the Union and give them everything they want," rather than, "Let them go," because that would also give them everything they wanted anyway. There were "Copperheads"/"Peace Democrats" like Clement Vallandigham of Ohio who would have gladly taken a "peaceable separation" if it meant the end to the war. But he, and many others, lost re-election in 1862, as those voices became less popular. In fact, he was deported to the South for violating an ordinance in Ohio that forbade sympathizing with the enemy, after giving a pro-Southern speech in mid-1863. He was subject to a military trial, and then deported to the Confederacy, where he immediately surrendered as a prisoner of war, considering himself a U.S. citizen. He was then allowed to escape, made his way to Canada by an ocean voyage, and then ran for governor of Ohio from his place of exile. He lost in a landslide, getting less than 40% of the vote, though that still accounted for 187,000 votes of Ohioans.
But again, once the war started, Vallandigham and the types of people who supported him once the war broke out tended to want the North to compromise on the South's terms that would allow the South to rejoin the Union. "Peaceable separation" was secondary since it wasn't seen as any more attainable than reunion, despite basically requiring the same set of compromises either way. So other Copperheads like Franklin Pierce tended to play up national unity in advocating for the acceptance of the South's demands, as a more achievable peace than disunion was.
FURTHER READING:
Lincoln and the Decision for War: The Northern Response to Secession by Russell McClintock, 2010
Northern Editorials on Secession, Vols. 1 and 2 ed. by Howard Cecil Perkins, 1942