“We have never engaged in chest-beating on what we’re doing on terrorism,” said a White House official, who was pleased by how the interviews had played out. “But this dynamic where we’re responding to criticism from the former vice president gave us the opportunity to explain what we’re doing, without just going out and talking tough.”

And there is some evidence to suggest the strategy is working for Obama. A Washington Post poll released last week found that 56 percent approve of the way the president handles the threat of terrorism, making it Obama’s strongest core issue. Meanwhile his ratings on the domestic issues that got him elected slip: Only 45 percent approve of his handling of the economy, and 43 percent are with him on health care…

But to the White House, Cheney provides a particularly appealing foil. Administration allies see few drawbacks to vigorously rebutting him. Responding elevates the profile of one of Obama’s strongest critics, but so doing allows the administration to compare its policies against the most unpopular member of the Bush team.

“He is a polarizing figure, and I think the president looks pretty measured and strong and reasonable when stacked up to Cheney,” said Democratic pollster Jeremy Rosner.