Senate action on two of President Barack Obama’s top priorities this year — gun violence and immigration — will likely be delayed until April at the earliest, as budget issues yet again consume all of Washington’s political oxygen and capital.

Though Senate Judiciary Chairman Patrick J. Leahy, D-Vt., on Monday announced a Thursday markup for a series of gun bills, Congress must first address a March 27 deadline to avoid a government shutdown, the implementation of $85 billion in across-the-board spending cuts this year and a budget resolution. That means any gun violence measure is unlikely to hit the floor for another six weeks and that any immigration overhaul would be slated following the gun debate.

With the White House focused almost exclusively on pressuring Republicans to replace the sequester with a plan that includes targeted tax hikes, Senate aides suggested Monday that the president likely wouldn’t re-engage fully on gun issues until after budget matters had been resolved. Those aides added that any gun legislation won’t get the kind of significant consideration needed for passage until after the Easter recess.

In a precursor of speeches to come, Obama’s address to a bipartisan group of governors Monday was almost entirely centered on the sequester — there was no mention of gun control and only a passing mention of immigration.

“One thing I know unites all of us and all of you, Democrats and Republicans, and that is the last thing you want to see is Washington get in the way of progress,” Obama said. “Unfortunately, in just four days Congress is poised to allow a series of arbitrary, automatic budget cuts to kick in that will slow our economy, eliminate good jobs, and leave a lot of folks who are already pretty thinly stretched scrambling to figure out what to do.”

Meanwhile, Thursday’s Senate Judiciary markup will feature four separate gun bills. Moving separate measures, as opposed to one bill with multiple amendments, is part of a larger strategy to increase the odds that less controversial pieces might become law, according to aides tracking the issues. For example, Sen. Dianne Feinstein, D-Calif., will get a markup of her assault weapons ban, which could pass out of committee on a party-line vote only to fail in the full Senate.

Aides in both parties, however, suggested that the committee meeting will likely get pushed to next week because any senator can request a one-week delay in consideration of newly added agenda items. Ranking member Charles E. Grassley, R-Iowa, is expected to ask for such a postponement, but his office would not confirm whether he intends to do so.

“The committee rules allow any member to hold over a bill or nominee until the next business meeting. At this time, it’s unclear if any member, Democrat or Republican, will ask if any of the bills be held over, especially since the bills don’t appear to be ready for consideration,” a Grassley spokeswoman said in an email.

Judiciary’s roster of bills for Thursday appears to include a placeholder for a bipartisan deal on background checks. The author of the shell bill, New York Democratic Sen. Charles E. Schumer, has been working with Republican Sens. Tom Coburn of Oklahoma and Mark S. Kirk of Illinois and West Virginia Democratic Sen. Joe Manchin III on a potential compromise.

On Sunday, Coburn said he and Schumer were still far from agreement, but a delay in committee action would give the lawmakers about 10 more days to find a compromise.

“Well, I don’t think we’re that close to a deal, and there absolutely will not be recordkeeping on legitimate, law-abiding gun owners in this country,” Coburn told “Fox News Sunday.” “And if they want to eliminate the benefits of actually trying to prevent the sales to people who are mentally ill and to criminals, all they have to do is create a recordkeeping, and that will kill this bill.”

Schumer is hoping to include a provision that would require citizens to keep a personal record of their gun sales to other private citizens, much like gun stores already do. Even if Coburn and Schumer can come to an agreement before markup, it’s unclear whether the measure would receive broader GOP support in committee. Any background check bill — in compromise with Republicans or not — would likely be amended by the full Senate.

Leahy has been pressuring members with gun-related legislation to make haste. The longer the committee goes without approving legislation — and the longer Congress goes without doing so — the more difficult it will be for lawmakers to pass anything, the thinking goes. Between the attention to budget issues and the sheer distance from the tragic and politically catalyzing elementary school shooting in Newtown, Conn., Washington’s window could be closing.

Of course, the window isn’t that big to begin with, as Feinstein likely can attest. Her effort to reinstate the assault weapons ban has been largely dismissed as a nonstarter with Republicans.

“I recognize it’s an uphill battle,” Feinstein said Monday on MSNBC. “America’s laws are virtually nonexistent, and therefore I think this is a good bill. I intend to fight. I did it once before. If it doesn’t get done right now, be assured I will continue to press the case.”