The subject of Idaho's strange shape came up in conversation today, so I searched and found this page, which states that a proposal to incorporate the northern panhandle with Washington rather than Idaho got 96% of the vote there, and passed both houses of Congress, but was pocket vetoed by President Grover Cleveland. Why didn't Cleveland sign the measure? Did he actually have any opinion on the subject that we know of? I find it strange that such an apparently popular notion simply died on the president's desk.
The 96% vote of northern Idahoans was not a part of the bill that later passed through Congress in 1887. That 96% vote was done in 1878, and largely stemmed from residual anger towards the government in Boise for moving the capital from Lewiston to Boise in a very controversial act in 1864.
Regarding the bill Cleveland pocket vetoed, the territorial governor of Idaho at the time, Edward Augustus Stevenson, personally lobbied Cleveland to not sign the bill. Congress passed the bill with the reasoning that the two geographical sectors of the territory were no longer compatible with each other. The northern panhandle was dominated by natural resource industries, while the south was an agricultural-based economy. On top of that, the two regions of the territory were poorly connected through transportation and communication. In contrast, the northern panhandle and eastern Washington were much better connected with each other.
But Stevenson was intent on keeping the territory unified, as part of his desire to achieve increased national influence on behalf of the territory. His plea to Cleveland apparently worked, as Cleveland did not sign the bill. Stevenson also later campaigned against further efforts to try to break up the territory, all of which were of course successful, and Idaho eventually achieved statehood in 1890, rendering the question of removing the panhandle from Idaho and giving it to Washington moot.