In his poem "What to the Slave is the Fourth of July," he mentions the above quote re: Hungary. What was going on in Hungary that made Americans "ready to fly to arms" over?
Brief background: In 1848, a number of revolutions swept European countries (including Hungary); many of these political upheavals were aimed at removing monarchical systems and forming democratic or otherwise more liberal governments.(1)
In Hungary, revolutionaries attempted to gain independence from the Austrian Empire. Ultimately, with assistance from Russia (then ruled by Tsar Nicholas I), the Austrian emperor put down the revolution and restored imperial power. From 1849-50, a wave of Hungarian emigrants entered the United States; many of these were former revolutionaries facing backlash in Hungary.
Frederick Douglass delivered his speech, "What to a slave is the fourth of July?", in 1852: exactly the time when a famous Hungarian revolutionary was giving a speaking tour throughout the country. Lajos Kossoth was briefly the president of the independent Kingdom of Hungary in 1848. As an emigre in the US, he was hailed as a champion of liberty and a freedom fighter.
Meanwhile, Douglass said, when it came to abolitionists (also freedom fighters) who would speak out about "the ten thousand wrongs of the American slave, you would enforce the strictest silence, and would hail him as an enemy of the nation who dares to make those wrongs the subject of public discourse!"
When Douglass said that his listeners (white Americans) were so willing to "shed tears over fallen Hungary," he was talking about the outpouring of pro-Hungary sentiment in the media of his day. Douglass was pointing out the hypocrisy of criticizing oppression in Europe while millions of people (African American slaves) were oppressed in their own country, the United States.
(1) Mike Rapport, 1848: Year of Revolutions (2010)