President Obama has a credibility problem.

Weakened by ObamaCare's woes, the president has lost the trust of a majority of Americans as his approval rating has slipped to an all-time low. And while Obama's diminished standing will loom over his domestic policy agenda and his party's 2014 campaigns, it will also prove problematic for his ongoing engagement with Iran, as he'll have to win over a skeptical public on a thorny foreign policy issue.

Obama has acknowledged a need to "win back" the public's trust. And indeed, a spate of recent polls have consistently found that a majority of Americans — 53 percent in the latest CNN survey out this week — don't believe the president is "honest and trustworthy." Moreover, a similarly high percentage of Americans don't approve of how the president has handled foreign policy.

At the same time though, Americans are largely receptive to the idea of diplomatic engagement with Iran. Two-thirds of Americans support a deal to restrict, though not end, Iran's nuclear capabilities, at least in general terms.

Those competing views — the public's distrust of Obama, but its support for an Iranian compromise — could run against each other going forward. That's particularly likely given the backlash, already developing and sure to intensify, that Obama will endure for pursuing such an elusive, intangible goal of curtailing Iran's nuclear ambitions.

Republicans, almost uniformly, blasted the terms of the interim deal as a massive cave that would result in a nuclear Iran. The deal was a "mistake" that would "not stop Iran's march toward nuclear capability," House Majority Leader Eric Cantor (R-Va.) said in a statement. Sen. Marco Rubio (R-Fla.) was more critical, saying the easing of some sanctions had actually made "a nuclear Iran more likely."

Adding to Obama's difficulty, a plurality of Americans still believe Iran is an enemy that can't be trusted, even if they like the sound of a nuclear deal. It's in this environment that even Democratic lawmakers are still eyeing tougher sanctions for Iran to supplement the interim nuclear deal.

Sens. Bob Menendez (D-N.J.) and Mark Kirk (R-Ill.) are working on joint legislation that would reinstate the full weight of sanctions on Iran, and impose harsher ones if that nation fails to comply with the six-month agreement, even though the administration has warned that legislative action could undermine negotiations toward a long-term deal.

Yet, as with ObamaCare, the president's fragile standing has afforded even critics from his own party cover to oppose the administration. While that could be little more than political posturing, Obama will nevertheless have to expend energy and political capital rallying support behind the slog toward a long-term pact.

Obama has sought to tamp down the trust concerns by noting that the deal is specifically intended "to chip away at the mistrust that's existed for many, many years" between Iran and the U.S. First, though, the president will have to chip away at the mistrust a majority of Americans now have for him.