The No. 2 Senate Republican, in a video clip posted on YouTube showing the senator speaking to a local Tea Party crowd on Friday, said the president told him during a one-on-one meeting in the Oval Office that he was concerned he wouldn't win GOP support on immigration legislation if he took care of border security first.
"The problem is, he said, if we secure the border, then you all won't have any reason to support comprehensive immigration reform," Kyl said, as the crowd in the room gasped loudly. "In other words, they're holding it hostage."
"The president didn't say that and Senator Kyl knows it," Pfeiffer said in a written statement. "There are more resources dedicated toward border security today than ever before, but, as the president has made clear, truly securing the border will require a comprehensive solution to our broken immigration system."
Burton repeated the claim at the press briefing Monday afternoon.
But Kyl's office stood by the senator's account. Kyl spokesman Ryan Patmintra said, "There were two people in that meeting, and Dan Pfieffer was not one of them." He said Pfeiffer's call for comprehensive immigration legislation "only confirms" Kyl's story.
And later, Kyl himself affirmed to Fox News the accuracy of his version: “I portrayed our conversation totally accurately ... The president cannot say that what I said was incorrect.”
While Obama has pledged to send an influx of National Guard troops to the U.S.-Mexico border, Kyl said in the clip that the president made clear to him that border security is just a political tool in the broader goal of passing an immigration package through Congress.
In the town hall meeting, Kyl said he was "not so sure" the president's concern about GOP support was legitimate, but that regardless, the administration has an "obligation" to secure the border.
"They don't want to secure the border unless and until it is combined with comprehensive immigration reform," Kyl said. "They frankly don't want to do it. They want to get something in return for doing their duty."