April in Washington is supposed to be all about immigration and gun control, with potentially climactic moments on course for both. But those expectations will prove illusory in the first days after the House and Senate return from recess next week, when headlines will come from a couple of high-profile maneuvers in the budget wars.

The maneuvers will be largely meaningless, despite the headlines, but the consequences for the outcome could be immense, one way or the other.

First, President Barack Obama will deliver the details of his spending and revenue requests to the Capitol on April 10 — nine weeks after his fiscal 2014 budget was due and two weeks after the House Republicans and Senate Democrats got out in front of him with their own, largely irreconcilable documents.

Then, that night, the president is supposed to have dinner with a dozen GOP senators who have a perceived willingness to think outside the box of the party’s fiscal orthodoxy.

While combating gun violence and modernizing immigration law are his high-profile drives for the spring, Obama still holds out hope for an additional $1.5 trillion in long-term deficit reduction. Locking that down would assure his legacy as an economic steward and promoter of job growth.

Hosting such a meal on the day of his budget submission will, of course, be portrayed as the president trying one final time to jump-start talks for an elusive “grand bargain.” That may be true to a point, and dinner organizer Johnny Isakson of Georgia may be able to find 11 accomplishment-driven and politically safe Republicans to create an enchanted evening.

But it’s much more likely the dinner will produce no more agreement than on the virtues of candid talk over a nice supper.

Why? Both the White House and Isakson are downplaying expectations that the dinner will do any more than kindle good feelings about future gatherings. The guest list is supposed to be totally different from the roster for Obama’s first “charm offensive” dinner a month ago, which featured most of the usual centrist suspects.

And GOP leaders will by then probably have dismissed the Obama budget books as barely worth the hackneyed “dead on arrival” response from Congress.

You can already see this one coming. Obama’s budget will propose ways for raising hundreds of billions in new money to slow the deepening of the U.S. debt. The GOP reaction to that one chapter will dominate the mainstream coverage. And it will be plenty vituperative, even though his ideas will be all about limiting or ending tax breaks and shelters for relatively narrow business niches; will be more modest than the $1 trillion called for in the Senate budget; will make no mention of raising rates and will be offered in the context of working with Congress to overhaul and simplify the IRS code.

The Republicans’ wall of resistance to allowing a second tax increase, on top of the $600 billion they acquiesced to on New Year’s Day, looks to be totally solid in the House and decently thick in the Senate. Senate Republicans will be joined by at least four of the five red state Democrats up in 2014.

The storyline of the perpetuated revenue stalemate is so easy for the media to explain that it stands to overwhelm the important potential news in Obama’s budget, which may carry a significant overture to the Republicans on entitlements.

The president has been signaling he’d support — though only as part of a big deal that included taxes, mind you — an eventual combining of the different Medicare coverage systems for hospitals and doctors. Doing so would increase out-of-pocket costs for the elderly, but it could also finance a new federally guaranteed cap on their total expenses, while also limiting the need for many of them to buy Medigap supplementary insurance.

Obama offered to negotiate on this two summers ago, but after those grand bargain talks collapsed, his gesture was largely forgotten. It’s back now in part because House Majority Leader Eric Cantor, R-Va., has been trying to resurrect the same sort of idea. Along with their shared openness to limiting Social Security benefit increases through the so-called chained consumer price index, the Medicare move would generate several hundred billion in entitlement savings.

This all assumes, of course, that Obama could get a decent share of Hill Democrats to vote for the changes along with the GOP mainstream.

It’s still a long shot and it will take some time beyond next week’s budgetary show pieces to come together. But the waiting should be over by July.

If there’s no deal before the next required increase in the debt limit, the long-term budget debate will be effectively ended until the next president takes office.