The United States is "resolutely opposed" to the bill, reintroduced this month after failing in 2009. "Our position is clear," State Department spokeswoman Hilary Renner said.
But such outside pressure from the United States and other Western nations has triggered a backlash of resentment from some in Uganda who view it as intrusive, The New York Times reported Wednesday.
Kizza Besigye, an Ugandan opposition leader, said Western lobbying on the issue was "misplaced" and "even annoying."
"There are more obvious, more prevalent and harmful violations of human rights that are glossed over," Besigye said. "Their zeal over this matter makes us look at them with cynicism to say the least."
The Obama administration has said it would use its diplomatic tools, including aid, to promote equal rights for lesbian, gay, bisexual and transgender people worldwide. British Prime Minister David Cameron also has threatened halt aid to countries that do not accept homosexuality.
The threat of pulling aid could produce unintended results, one expert suggests.
"While covert behind-the-scenes donor pressure on the Ugandan government has been useful in the past," said Rahul Rao, a lecturer at the Center for International Studies and Diplomacy in London, "overt pressure can be extremely counterproductive."