Tape recordings of the Supreme Court’s second day of gay marriage arguments are going to get the bulk of the Wednesday media coverage. The tapes with more immediate effect on Washington’s agenda will be coming out of the White House.

The court releases its old-media audio tapes this afternoon, following morning oral arguments in the case challenging the constitutionality of the Defense of Marriage Act. That will give the country a buffet of sound bites to speculate about what the justices will decide in a ruling that probably won’t be handed down for another 13 weeks.

At 6:30 p.m., though, Spanish-language Telemundo and Univision television networks will air the 15-minute interviews they’re video taping at mid-afternoon with President Barack Obama. As USA Today’s David Jackson writes in his blog, The Oval, Obama is likely to make indisputably clear news with whatever he says about his drive for an overhaul of the nation’s immigration laws.

Already this week, the president has challenged Congress to “finish the job” of writing legislation combining tighter border security with a pathway to citizenship for the 11 million illegal immigrants now in the country. Presumably, Obama will use this TV time to once again spur action from lawmakers and to incite agitation from the network’s target audience, thousands of whom are getting face time with their House members and senators during the current spring recess.

Beyond that generalized agitation, look for Obama to send a clear signal about something he worries is missing and wants to make sure gets into the bills before separate bipartisan groups in the House and Senate release their proposals. He’ll probably have something to say about one or more of the following:

• the coupling of a new citizenship process with proof of improved border security;
• the number of steps or length of time for an immigrant hoping to move from illegality to total legality;
• the finer points of a new guest worker program that must please both labor-strapped businesses and abuse-worried labor groups.

Whichever it is, the president will urge congressional negotiators to figure it out before Congress reconvenes on April 8, a mere three weeks before its next week away from Washington.

Conventional wisdom is already forming in the concurrent gun-control debate that Obama allowed too much time to pass since the Sandy Hook Elementary massacre, and so he is partially to blame for the foundering of significant legislative remedies. He doesn’t want the same squandered-the-momentum narrative to develop on immigration.

That’s the risk if a comprehensive deal isn’t unveiled on at least one side of the Capitol within days of lawmakers’ return April 8. Just this Tuesday, Sen. John McCain said, “I can’t guarantee anything” when asked to commit to a timetable for releasing the legislation he and others in the Senate’s “gang of eight” have been working on all year. They had been promising would be ready right after the spring recess.

McCain and Arizona’s other GOP senator, Jeff Flake, are spending Wednesday hosting a Mexican border security fact-finding strip with two Democratic senators in their negotiating group, Charles E. Schumer of New York and Michael Bennet of Colorado. Expectations are getting dimmer the day trip will lead to a breakthrough that would guarantee Judiciary Committee action by the end of next month.

If that deal doesn’t materialize soon, attention will turn to a parallel group of negotiators in the House. Some of them have said for weeks that they are “this close” to a deal that could pass with bipartisan support. But every day without a triumphant news conference, and the accompanying silence about the cause of the holdup, makes their ability to capitalize on the politically ripe moment as elusive as the Senate’s.

In other words, if the congressional haggling that Obama has been staying away from comes to naught, he’s the one who stands to be assigned most of the blame.