Maybe it’s just awkward timing dictated by the White House media management team. But the excerpts of an interview President Obama gave ABC on Tuesday — broadcast this morning just hours before his meeting with House Republicans — amount to a sodden wet blanket on all the mildly optimistic talk about a grand budget bargain this year.

The president described his forays to the Capitol this week as efforts to reach “the common-sense caucus” in both parties, whom he views as insufficiently aware (thanks to their leaderships) of the sincerity of his interest in reaching a deal or his outline of what he’d agree to. Other than pointing out the available middle ground, he said, there is nothing he can do to force lawmakers on either side to get there.

And — laying the blame squarely on the GOP — Obama held out much less hope for a deficit compromise than he has during his past week of reach-outs to the Republicans. If the Ryan budget is more than an appeal-to-the-base political document and continues to be the party’s barely alterable position, the president signaled, then his efforts at accommodation will have quickly come to naught. And the more he’s at the center of the talks, he said, the more likely the GOP right would spurn and then kill whatever agreement might get reached.

“At some point I think I take myself out of this; right now what I’m trying to do is create an atmosphere where Democrats and Republicans can go ahead and get together,” the president told “Good Morning America” host George Stephanopoulos. “But, ultimately, it may be that the differences are just too wide. It may be that, ideologically, if their position is, ‘We can’t do any revenue,’ or, ‘We can only do revenue if we gut Medicare or gut Social Security or gut Medicaid,’ if that’s the position, then we’re probably not going to be able to get a deal.”

But that won’t “create a crisis,” at least in the short term, he added. “It just means that we will have missed an opportunity.”

This latest twist in Obama’s approach-avoidance attitude toward fiscal dealmaking is sure to give Republicans a case of skeptical whiplash. For the past week, many of them have been professing to a readiness to give the presidential outreach the trust-but-verify treatment — especially because he’s been quite specific about what things-that-make-liberals-furious he’d be willing to endorse in the name of compromise. Curbing the growth of Social Security benefits by adopting a new government gauge for inflation is Exhibit A on that front.

Now, many of these same Republicans will lament that they’re being played by a president willing to sound accommodating just often enough to keep his approval ratings from slipping below the symbolic 50 percent mark.

Oh-oh. Look here.