WASHINGTON — The fight between President Barack Obama and congressional Republicans over the automatic spending cuts that start next week is shifting from one about stopping them to one about assigning blame if they happen.

Obama on Tuesday surrounded himself with firefighters and other first responders at the White House, where he said Republicans would be at fault if the spending reductions take effect and cost the jobs of emergency personnel. The campaign-style event marked the beginning of what aides described as an intensifying push to pressure Congress to postpone the cuts — or to blame Congress if it doesn’t.

Republicans fought back by seeking to portray Obama as the mastermind of the spending reductions, known as the sequester, thereby making him responsible for any damage they cause to the military and the economy

The escalating efforts are a reflection of how crucial the sequester has become in the long-running debate over the size and scope of the federal government.

No matter how the idea came about, the $1.2 trillion in cuts to defense and domestic spending will nevertheless serve as a high-profile test of the deep cuts that Republicans have been pushing for years.

If the cuts are instituted and Americans do not see them as a major problem, that could serve as an affirmation of the GOP view that the government is unnecessarily big and a hindrance to private-sector growth. If there is a significant backlash, public sentiment is likely to shift toward the Democrats, who generally see the government as a positive force.

The sequester is the result of a summer 2011 deal between Obama and Congress that was designed to be so distasteful that it would compel lawmakers to agree on a broader framework to tame federal borrowing.

That hasn’t happened. And with no communication between the White House and congressional Republicans, much of Washington seems resigned to the cuts taking effect March 1.

The deal requires the government to dramatically trim spending on a wide range of domestic programs, including education as well as research and development. It would lead to the furlough of thousands of workers, officials say. And it would also sharply reduce spending at the Pentagon — a prospect that would help stabilize the federal debt over the next decade but that also creates deep anxiety among military leaders.

Macroeconomic Advisers, an independent economic group, said Tuesday that sequestration would cost 700,000 jobs and push the unemployment rate a quarter of a percentage point higher than it otherwise would have been.

The group said in its analysis that the cuts would be a significant economic hit, given that taxes have already gone up this year and “with the economy still struggling to overcome the legacy of the Great Recession.”

Obama said he prefers to delay the sequester through the end of the year by trimming other spending, such as farm subsidies, and raising more money by limiting breaks and loopholes that favor top earners and select industries, such as oil and gas companies.

“So far, at least, the ideas that the Republicans have proposed ask nothing of the wealthiest Americans or biggest corporations, so the burden is all on first responders or seniors or middle-class families,” Obama said Tuesday. “They double down, in fact, on the harsh, harmful cuts.”

Senior administration officials say they have the upper hand in the debate because Americans have shown their broad support, in polls and at the voting booth, for asking the wealthy to pay higher taxes rather than just cutting government services.

“So now Republicans in Congress face a simple choice,” Obama said Tuesday. “Are they willing to compromise to protect vital investments in education and health care and national security and all the jobs that depend on them? Or would they rather put hundreds of thousands of jobs and our entire economy at risk just to protect a few special-interest tax loopholes that benefit only the wealthiest Americans and biggest corporations?”

Leading Republicans, however, were pointing the finger directly at the president.

“The president offered no credible plan that can pass Congress— only more calls for higher taxes,” House Speaker John Boehner, R-Ohio, said Tuesday. “Washington Democrats’ newfound concern about the president’s sequester is appreciated, but words alone won’t avert it.”

Republicans believe they are well positioned because Obama needs their support to avoid the spending cuts, which are set to happen automatically, and they believe Obama will be blamed for the negative effects.

Three GOP senators wary of defense cuts — John McCain of Arizona, Lindsey Graham of South Carolina and Kelly Ayotte of New Hampshire— said Tuesday that Obama was overtly playing politics with the sequester.

“Today, just 10 days prior to the implementation of these draconian cuts, the president held another campaign event to blame Republicans for sequestration, which was actually his idea in the first place,” they said in a joint statement. “This country needs a commander-in-chief, not a campaigner-in-chief.”

Time is running short to stop the sequester, with lawmakers not planning to return to Washington until Monday.

Republicans say more taxes are out of the question, while administration officials said Tuesday that they could not imagine a compromise that does not open the door to higher taxes on the wealthy.

“Senate Republicans are going to have to spend this week explaining to their constituents why they would rather see sequestration hit than support the Democrats’ bill to replace it with a balanced mix of responsible spending cuts and new revenue from the wealthiest Americans,” said Sen. Patty Murray, D-Wash., chairwoman of the Senate Budget Committee.

Over the long term, Obama wants to replace the sequester with cuts to Medicare and other mandatory spending programs and hundreds of billions of dollars in new tax revenue achieved through limiting deductions benefiting wealthy Americans and corporations.

Republicans favor a plan that would trim domestic and mandatory spending while largely sparing defense spending. Republicans want to limit deductions through an overhaul of the tax code, too, but they want to use any new tax revenue generated through that process to lower tax rates.

The GOP also wants to balance the budget within a decade, which, budget experts say, would require spending cuts far in excess of those in the sequester.