Thanks for asking - I'm sitting on the Gallaudet campus as I type this and I'm always happy to answer questions about it.

Gallaudet is not the only higher education institution for the Deaf - others exist in New York, Japan, China, and elsewhere - but it is the world's only liberal arts university designed exclusively for deaf and hard of hearing students.

Calls for the establishment of a college for Deaf students began in the 1850s. Students were graduating from secondary schools all over the country, but had nowhere to go to further their education. Deaf artist John Carlin published an essay in the American Annals of the Deaf and Dumb in 1854, stating that Deaf people could rise to great heights if only they had more education, and encouraging discussion of the topic in the community. Krentz writes that Carlin, despite being at pretty great heights himself, had an inferiority complex, and it is likely these feelings that prompted him to call for a way for deaf people to be more than manual laborers (as they usually were at the time).

Carlin's essay did in fact prompt a national conversation in the Deaf community, as cataloged by the Little Paper Family (Deaf school newspapers). When Edward Miner Gallaudet came to Washington DC as a 20-year-old (in 1857) to run the Columbia Institution for the Deaf, he was well aware of this conversation. He immediately began building federal support of the school, including student performances for members of Congress, and taking the members out to dinner at every opportunity. Even through the Civil War, he was able to increase the Congressional appropriation year after year. So when he asked Congress to support a college, they were already pre-disposed thanks to his lobbying skills.

James McPherson says that Abraham Lincoln most likely signed the charter for Gallaudet eagerly, because it was in line with his existing interests in promoting equality and opportunity for minorities in the US. From an 1861 address to Congress:

that form and substance of government, whose leading object is, to elevate the condition of men— to lift artificial weights from all shoulders— to clear the paths of laudable pursuit for all— to afford all, an unfettered start, and a fair chance, in the race of life.

But other than the work described above, the hearing community was not particularly invested in the creation of a university for Deaf people. We have a lot of record of Deaf people calling for one, and the actual creation got some coverage in hearing newspapers, but the only hearing people who were particularly interested in getting Gallaudet established were those already involved with the Deaf community as teachers, family members, etc.

For more, see A Fair Chance in the Race of Life, Greenwald and Van Cleve, eds. (Esp. Krentz, De Lorenzo, and McPherson)