Thats a distinctly un-American way of looking at it. I don't mean to insult with that statement by the way, just wanting to point out that's not American logic, especially in that time period. You are also forgetting Maine volunteers. What do you think that is going to do to New England regiments fighting in the war, especially those from Maine?
No insult taken, however, you also nail a good point that the people of Maine will be
distinctly unhappy overall. That being said, since mid 1862 much of Maine has already been occupied by the British, so the relief of seeing the British gone will also be a big relief for them overall. The loss of Aroostook (and to be determined territory up to Machias Bay) is, in comparison, a bit more palatable than uncertain occupation. Not to say they won't be pretty mad after the fact.
Respectfully, I can not see Lincoln pushing this if the Union was showing signs of holding there own, even if they had some losses. It just doesn't fit the American persona.
Well, nations can have personas, but in the cold hard truth of war and economics, some things are inevitable. In this case, there is a much larger economic-strategic picture that it is also worth keeping in mind. Since the British entry into the war in February of 1862 the United States has had to divert over 150,000 men (or roughly 25% of the men mobilized to fight come early 1862) who would otherwise be fighting the Confederacy to invade Canada or hold off British attacks in the coasts or in Maine. The invasions of Canada East have been bloody fiascos which were all repulsed, while the British invasion of 1863 was, eventually, stopped at Saratoga it has sealed up the only effective invasion route to deal a defeat to the British. In Canada West the invasion was successful in pushing up to the Bay of Quinte before stalling at the Battle of Mount Pelion, but then a lack of resources to continue the invasion meant the US had to fall back on Toronto, where they have been staring daggers at the British 3rd Corps, but to do much more would require more resources which the armies fighting the Confederacy on the Mississippi desperately need.
The strategic initiative in the West in early 1862 shifted to the Confederacy which, while having mixed results, ended in a semi-successful invasion of Kentucky and eventually forced the Union to abandon Nashville. While Grant was able to then pivot and capture Memphis, the offensives stalled, and he then had to move again because of Confederate naval superiority on the Mississippi River. In doing so he had to scorch the earth, then ended up turned back at Corinth, but holding western Kentucky for the Union. Now though, a new Confederate offensive will be coming in 1864, and the soldiers currently occupying Canada would be very useful to stop that.
In the Eastern theater, the war nearly ended in the summer of 1863 as the joint Anglo-Confederate offensive against Washington placed the capital and Baltimore under threat, and it was only by shifting forces from out West - as none could be moved away from Maine or the ongoing fight against the British invasion of upper New York - that Lee's siege was broken and the capital/Army of the Potomac saved. Now Lee has knocked them back on their heels again, and reinforcements are desperately needed once more. The avenue to turn to is either more conscription (something that proved unpopular already) or moving the forces which would otherwise be fighting the British.
That doesn't begin to get into the economic outlook however. Despite Farragut's victory at Sandy Hook, the blockade still strangles the American coasts and prevents them from trading with the outside world or using the coasts as a trade network, thus putting more pressure on American railroads which are already overtaxed. This has, as I've outlined in regular chapters, caused inflation (in Chapter 75, 300 greenbacks is worth 100 dollars gold), contractions in the consumer markets, and farms to fail forcing many out of their homes and into the frontier. It's stretching the economy of the United States to the breaking point so while many want to continue the war, the Peace Faction in the Democratic Party is already more popular simply because so many are being driven to economic privation. There are those who want peace at any cost TTL.
All these factors combined are weighing heavily on Lincoln's mind, which means he has to start making tough decisions in 1864. He could, in theory, repudiate the treaty and decide to fight to the bitter end, but doing so may well cost him the election in November, and there's no guarantee that fighting on at the moment would improve the military situation. Worse, despite all this he must still defeat the Confederacy at the same time.
In light of all the above, I still believe that Lincoln is getting a bargain. Though when I post the text of the Treaty of Rotterdam I'll still leave you to be the judge!