WASHINGTON — With big, automatic budget cuts about to kick in, House Republicans are turning to mapping strategy for the next showdown just a month away, when a government shutdown instead of just a slowdown will be at stake.

Both topics are sure to come up at the White House meeting Friday between President Barack Obama and top congressional leaders, including Republican House Speaker John Boehner. A breakthrough on replacing or easing the imminent across-the-board spending cuts still seems unlikely at the first face-to-face discussion between Obama and Republican leaders this year.

To no one’s surprise, even as a dysfunctional Washington appears incapable of averting a crisis over economy-rattling spending cuts, it may be lurching toward another over a possible shutdown.

Republicans are planning for a vote next week on a bill to fund the day-to-day operations of the government through the Sept. 30 end of the 2013 fiscal year — while keeping in place the new $85 billion in cuts of 5 percent to domestic agencies and 8 percent to the military.

The need to keep the government’s doors open and lights on — or else suffer the first government shutdown since 1996 — requires the GOP-dominated House and the Democratic-controlled Senate to agree. Right now they hardly see eye to eye.

The House GOP plan, unveiled to the rank and file on Wednesday, would award the Pentagon and the Veterans Administration with their line-by-line budgets, for a more-targeted rather than indiscriminate batch of military cuts, but would deny domestic agencies the same treatment. And that has whipped up opposition from veteran Democratic senators on the Appropriations Committee. Domestic agencies would see their budgets frozen almost exactly as they are, which would mean no money for new initiatives such as cybersecurity or for routine increases for programs such as low-income housing.

“We’re not going to do that,” said Sen. Tom Harkin, D-Iowa. “Of course not.”

Any agreement needs to pass through a gantlet of House tea party conservatives intent on preserving the across-the-board cuts and Senate Democrats pressing for action on domestic initiatives, even at the risk of creating a foot-tall catchall spending bill.

There’s also this: GOP leaders have calculated that the automatic cuts arriving on Friday need to be in place in order for them to be able to muster support from conservatives for the catchall spending bill to keep the government running. That’s because many staunch conservatives want to preserve the cuts even as defense hawks and others fret about the harm that might do to the military and the economy. If the automatic cuts are dealt with before the government-wide funding bill gets a vote, there could be a conservative revolt.

“The overall sequester levels must hold,” said Rep. Tom McClintock, R-Calif.

Little to no progress has been made so far between House and Senate leaders and the White House, and given the hard feelings engulfing Washington, there’s no guarantee that this problem can be solved, even though the stakes — a shutdown of non-essential government programs after March 27 — carry more risk than the across-the-board cuts looming on Friday.

The funding plan for the rest of the fiscal year will be a main topic at the White House meeting on Friday, the March 1 deadline day for averting the across-the-board cuts.

Obama, speaking to a group of business executives Wednesday night, said the cuts would be a “tumble downward” for the economy, though he acknowledged it could takes weeks before many Americans feel the full impact of the budget shrinking.

The warring sides in Washington have spent this week assigning blame rather than seeking a bipartisan way out. In a glimpse of the state of debate on Wednesday, Republicans and the White House bickered over whether the cuts would be under way by the time Friday’s meeting started. A spokesman for Boehner said they would be in place; the White House countered that Obama would in fact have until midnight Friday to set them in motion.

The cumbersome annual ritual of passing annual agency spending bills collapsed entirely last year — not a single one of the 12 annual appropriations bills for the budget year that began back in October has passed Congress — and Congress has to act by March 27 to prevent a partial shutdown of the government.

By freezing budgets for domestic agencies, the Republican plan would deny an increase for a big cybersecurity initiative, additional money to modernize the U.S. nuclear arsenal and money to build new Coast Guard cutters. GOP initiatives such as more money for the Small Business Administration or fossil fuels research would be hurt as well, but there’s little appetite for the alternative, which is to stack more than $1 trillion worth of spending bills together for a single up-or-down vote.

But the GOP move to add the line-by-line spending bills for the Pentagon and veterans’ programs to the catchall spending bill would give the military much-sought increases for force readiness and the Veterans Administration additional funding for health care.

That approach has few fans in the White House, which is seeking money to implement Obama’s signature efforts to overhaul financial regulation and the nation’s health care system, or within the Democratic Senate, where members of the Appropriations Committee want to add a stack of bills covering domestic priorities such as homeland security, NASA and federal law enforcement agencies like the FBI.

“You need balance,” said Sen. Charles Schumer, D-N.Y. “We feel as strongly about the domestic side as we do defense.”

The catchall spending measure, known as a continuing resolution or CR inside Washington, was originally seen as a potential must-pass measure to avert Friday’s cuts or make them less severe. But no serious talks to avert the cuts have been under way.

On Thursday, Democrats will force a vote on a measure that would forestall the automatic cuts through the end of the year, replacing them with longer-term cuts to the Pentagon and cash payments to farmers and installing a minimum 30 percent tax rate on income exceeding $1 million. But that plan is virtually certain to be toppled by a GOP-led filibuster vote.

Republicans in turn are considering offering a measure that would give Obama authority to propose a rewrite to the 2013 budget to redistribute the cuts. Obama would be unable to cut defense by more than the $43 billion reduction that the Pentagon currently faces, and would also be unable to raise taxes to undo the cuts. The GOP plan would allow a resulting Obama proposal to go into effect unless Congress passed a resolution to overturn it.

The idea is that money could be transferred from lower-priority accounts to accounts funding air traffic control or meat inspection. But the White House says that such moves would offer only slight relief. At the same time, however, it could take pressure off of Congress to address the sequester.

In the House, where Republicans in the past Congress passed legislation to replace the cuts, Boehner has said it’s now up to Obama and the Senate to figure a way out. The Senate never took up the House-passed bills, which expired when the new Congress was seated in January.