Story highlights CBS airs "60 Minutes" interview with President Obama

Obama: The GOP thought its "best bet" was inaction, thinking the economy will worsen

He laments what he calls a dearth of "honest conversation" in Washington

He says Gingrich has been around "a long time" and Romney has "lot of practice" in politics

President Barack Obama accused Republicans of making a blunt political calculation after his election three years ago, deciding to resist his initiatives, skirt compromise and bank on the economy getting worse to bolster their re-election prospects.

Openly speculating in a CBS interview on the GOP's strategy, Obama said Republications decided: "Our best bet is to stand on the sidelines because we think the economy is going to get worse and, some point, just blame him (Obama)."

"So we haven't gotten the kind of engagement that I would have liked, " Obama said in the interview that aired Sunday on CBS's "60 Minutes."

The president tried to frame what he predicted will be a "great debate" next year, when he's up for re-election, as a "stark" choice between "a system in which the people who have benefited the most (should) do a little bit more, or they (should) not."

"Do they think that cutting taxes further -- including on the wealthy (and) cutting taxes on corporations -- gutting regulations: Do we think that is going to be more successful?" Obama asked rhetorically. "If the American people think that's going to be the recipe for success ... then I am going to lose."

The president lamented what he described as a lack of "honest conversation about the greatest income inequality since the 1920s" or who and what was responsible for "the worst financial crisis since the Great Depression."

He dismissed Republican criticisms he has been engaging in class warfare or promoting socialism. Focusing on making life easier, fairer and more prosperous for middle class citizens should be a shared goal, the president said.

"What's happened to the bargain, what's happened to the American deal that says we're focused on building a strong middle class?" Obama said.

JUST WATCHED Obama urges payroll tax cut extension Replay More Videos ... MUST WATCH Obama urges payroll tax cut extension 03:25

JUST WATCHED Santorum: Obama foreign policy weak Replay More Videos ... MUST WATCH Santorum: Obama foreign policy weak 02:25

Recent polls suggest that the president's approach is not resoundingly resonating among the American public. His disapproval ratings in two polls taken last week -- from Gallup and Rasmussen -- were at 50% or higher, for instance.

Obama said that such sentiments are to be expected, given that economy is not "moving in a way that benefits everybody, as opposed to just a few." And he also said that it would take many years, and perhaps multiple presidents, to turn around the economy and change the culture in Washington.

"I'm the captain ... on the ship, and it's going through really bad storms," he said. "Even if we'd done the right things, if people's reality right now is still difficult, they're going to be frustrated."

At the same time, the president gave no indication that his policies hadn't been universally successful -- from stimulus and other efforts to prevent an economic depression, to new financial regulations, the auto bailout and health care reform.

"We did all the right things to prevent another Great Depression and to get the economy growing again, and to get job creation again," said Obama, noting the economy has grown for each of the past nine quarters. "But it hasn't made up for the hole that was created in the six, nine, 12 months before my economic policies took effect."

The president suggested it didn't matter who emerged from the Republican primary as his 2012 challenger, saying that all the candidates share the same "core philosophy." Still, he did characterize the two front-runners by name as veteran politicians.

"(Former House Speaker Newt) Gingrich is somebody who has been around a long time and is good on TV and is good in debates," Obama said. "But (former Massachusetts Gov.) Mitt Romney has shown himself (as being) good at politics as well. He's had a lot of practice at it."