Obama and McCain spar over immigration as they make pitch to Hispanics.

WASHINGTON–Sen. Barack Obama told an influential Hispanic group on Tuesday that White House rival Sen. John McCain — a champion of comprehensive immigration reform Congress has refused to pass — has let them down, while McCain’s allies disputed Obama’s claim that he was a key fighter in trying to get the hot-button measure approved.

The two White House rivals spoke — separated by a few hours — to the United Latin American Citizens convention here, the second time in two weeks they pitched themselves to a major Hispanic association, with each booked at another Hispanic conference later this month.

McCain drew the ire of the right wing of his party –conservatives whose support he now wants to solidify — when several years ago he teamed up with Sen. Ted Kennedy on a bill President Bush would have signed that would have provided a legal way for millions of illegal immigrants to stay in the U.S.

After a long battle, the measure failed in the Senate. Another try — where McCain did not play as prominent a role — did not produce a bill.

After two failed attempts, McCain now is in favor of Congress first dealing with border security. McCain is making a tactical retrenchment, not changing his support for immigration reform.

“I and many other colleagues twice attempted to pass comprehensive immigration legislation to fix our broken borders,” McCain told the group, with lawmakers against the package because “many Americans, with good cause, did not believe us when we said we would secure our borders, and so we failed in our efforts.”

McCain did not mention Obama by name, but Obama did bring up McCain when he took to the stage.

“Now, I know Senator McCain used to buck his party on immigration by fighting for comprehensive reform, and I admired him for it. But when he was running for his party’s nomination, he abandoned his courageous stance, and said that he wouldn’t even support his own legislation if it came up for a vote,” Obama said.

Obama repeated a claim he had been making: “I fought with you in the Senate for comprehensive immigration reform.” That assertion, tested by the Washington Post, yielded a story last March that concluded Obama “embellished” his role as a player.

A McCain surrogate, Rep. Lincoln Diaz-Balart (R-Fla.) seized on this in a conference call. Obama was “consistently and absolutely AWOL, nowhere to be seen in any of the meetings that we held on this issue of immigration.”

The Obama campaign, asked to respond to the charge he took too much credit, cited a February letter from the American Immigration Lawyers Association commending Obama for stressing the need for new immigration laws in his presidential campaign.