Final answer:
The letter of protest and petition from the Hawaiians did not convince American leaders to back off from annexing Hawaii due to the presence of US soldiers, the changing political climate after the outbreak of war, and President McKinley's maneuvering of the treaty.
Step-by-step explanation:
The letter of protest written by Queen Liliuokalani and the Hawaiians petitioning against the annexation of Hawaii did not convince American leaders to back off due to several reasons.
Firstly, there was a strong presence of US soldiers in Hawaii, and any armed resistance by the Hawaiians would have likely ended in failure and bloodshed.
Secondly, the political climate in the United States changed after the outbreak of war with Spain in 1898. Hawaii's strategic location halfway between the West Coast and the Spanish-controlled Philippines made it valuable to the United States.
Lastly, President William McKinley, who supported annexation, maneuvered the annexation treaty through Congress in 1898, taking advantage of a resolution that required a simple majority vote instead of a two-thirds majority.