U.S. President Barack Obama invoked blue-collar workers on Tuesday to contrast himself with his Republican challenger Mitt Romney.

Romney struggled to steady his reeling White House campaign after a secretly recorded video showed him dismissing Obama's supporters - almost half the country's voters - as victims who are too dependent on government.

Obama chided Romney on "Late Night with David Letterman" for the comments, and talked about the hard work of single mothers and auto workers.

After his television appearance, Obama spoke at a fundraising reception hosted by entertainment power couple Jay-Z and Beyonce at Jay-Z's 40/40 Club in Manhattan. Tickets for the event cost $40,000 each, and the Obama campaign estimated that there were about 100 people in attendance.

On Monday, a video surfaced of Romney showing him telling wealthy donors that almost half of Americans “believe they are victims” entitled to extensive government support. He said that as a candidate for the White House, “my job is not to worry about those people.”

On Tuesday, another video surfaced in which the Republican candidate told donors that the Palestinians have no interest in peace with Israel, and that they are committed to its destruction and elimination.

On Sunday, the American Israel Public Affairs Committee thanked elected leaders including the president for "steadfast" support of Israel.

"With Israel and America facing unprecedented threats and challenges in the Middle East, we deeply appreciate the close and unshakeable partnership between the United States and Israel. President Obama and the bipartisan, bicameral congressional leadership, have deepened America’s support for Israel in difficult times," said the statement issued shortly before Rosh Hashanah started on Sunday afternoon.

"Under the leadership of Democrats and Republicans, working together, U.S.-Israel security cooperation has reached unprecedented levels," the statement said.