According to an article in Politico:
A video is making the rounds of conservative blogs in which Sen. Jon Kyl (R-Ariz.) alleges that President Barack Obama told him that the administration will not secure the border unless it is part of comprehensive immigration reform.
... the Arizona Republican is seen telling supporters in North Phoenix that in a private meeting in the Oval Office, Obama said “the problem” with border enforcement measures is that “if we secure the border then [Republicans] won’t have any reason to support comprehensive immigration reform.”
White House Communications Director Dan Pfeiffer flatly denies it:
The President didn’t say that and Senator Kyl knows it. 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.
This is as close as you will come in politics to one side calling the other a liar.