The president’s with the two minority caucuses ­in Congress this afternoon — a lobster and blueberry pie lunch with the Senate Republicans and coffee with the House Democrats 90 minutes later — will bring an anticlimactic pause on the Obama courtship of Congress.

After three trips to the Capitol in as many days, and two intimate meals with senior Republicans last week, Obama will have no tangible deal to announce, and not even any professed promises of newfound GOP collaboration to boast about. Instead, the best he’ll be able to claim is that he’s made some inroads on doing better at legislative relations in his second term, and that he’s laid the predicate for more substantive bargaining in coming months.

Not just on the budget, but also on immigration and gun control. And not only with the Republicans, but with his more liberal fellow Democrats as well. Achieving even that much, if it holds, will have been worth the time and extra calories.

He’ll have a tough time getting much credit with the electorate for the intangible benefits of his efforts. That’s because many in the public still don’t quite understand the depth of his trust deficit at the Capitol, especially but not exclusively among the Republicans.

It is so bad that, when he made the relatively unimpeachable point to House Republcians yesterday that an immigration overhaul would boost their political standing more than his own, the observation was met with a roomful of chuckles. The GOP rank-and-file don’t trust his motives even when he says that he knows they don’t trust his motives. And that’s why he’s trying to be transparent with them — by conceding, at another point, that it would be easier for him politically to cultivate their differences rather than propose limitations that are already rattling his own base of support, on the Hill and in the country.

It’s a reverse Midas touch that will take an enormous amount of patience and finesse for Obama to overcome, and an enormous amount of goodwill and faith for the GOP to absolve him of. None of those four personality qualities has been a hallmark of federal policymakers for years, and even if they all materialize this spring, the ideological chasms between the two sides will remain enormous.

But if the president relaxes his “charm offensive” for very long at all, the chances for any legislative rapproachment will quickly fall out of reach