Democratic Sen. Charles E. Schumer said Wednesday he and Republican Sen. Lindsey Graham are “getting real close” to a deal on a comprehensive immigration overhaul.

Schumer said the two major unresolved issues are finding a second Republican sponsor and getting unions and business “on the same side” regarding how to handle the future flow of low-skill workers.

Schumer said finding more than one Republican to sponsor the bill — something Graham has insisted on — has been difficult. He said there are “four or five prospects we’re working on,” including John Cornyn of Texas. “We will not pass an immigration bill unless it’s bipartisan,” said, D-N.Y.

Graham, R-S.C., sounded less optimistic about the bill’s prospects. “There’s not a whole lot of appetite for immigration reform right now” among moderate Democrats and Republicans, Graham said. He added: “the president is going to have get more involved.”

Schumer and Graham are scheduled to meet Thursday with President Obama at the White House regarding the immigration bill.

Democrats face increasing pressure for signs of progress from immigration advocacy and Latino groups, who say a legislative blueprint should be made public prior to a March 21 rally to be held on the Capitol grounds. A coalition of grassroots immigration advocacy groups warned at a March 8 press conference at the National Press Club that Latino voters are growing frustrated.

“Millions of citizens and new Americans voted for change, and what they got, as far as immigration is concerned, is more, much more, of the same,” said Angelica Salas, executive director of Humane Immigration Rights of Los Angeles.