Never let it be said that President Obama has failed to spend time with Republican leaders in seeking an alternative to automatic budget cuts that are due to hit most federal departments Friday. On Wednesday, for example, the president gave GOP lawmakers as much as seven minutes, a rare face-to-face encounter that the White House described as a “meeting.”

The White House’s characterization of this momentary huddle at the Capitol as a meeting illuminates Mr. Obama’s strategy in dealing with Republicans on the budget cuts and other fiscal deadlines.

With speeches and other staged events, the president has tried to build public pressure for his agenda of tax increases coupled with spending cuts.

But he has made little time for negotiating directly with lawmakers who oppose his plans.

“It is a sincere conviction among Republicans that the president’s negotiating posture isn’t about getting a deal done, it’s a zero-sum political game where his aim is to destroy the Republican [House] majority in the next election,” said Steve Schmidt, a Republican strategist who served in 2008 as Sen. John McCain’s presidential campaign manager. “It’s certainly not an effective strategy for a leader in search of a deal.”

Since Mr. Obama’s contentious deficit-reduction talks with Republican leaders in 2011, which resulted in the “sequester” cuts set to take effect Friday, the president has been taking his case to the public on questions of taxation and spending.

Mr. Obama made his re-election campaign a referendum on his policies to aid the middle class and to force wealthier households to pay more, both for reducing deficits and for spending more on certain areas such as education, infrastructure and research.

Months before he won a second term in November, Mr. Obama predicted that his re-election would break the Republican “fever” that he viewed as the GOP’s knee-jerk opposition to his agenda. Since his victory Nov. 6, the president has been telling lawmakers who are fighting his efforts to raise taxes that elections have consequences.

His strategy worked in the “fiscal cliff” negotiations at the end of last year, resulting in a tax hike on households earning more than $450,000 per year and a temporary extension of the nation’s borrowing limit. There were few direct negotiating sessions with Republicans, the president preferring instead to call on the public to pressure GOP lawmakers into making a deal.

Now he is trying the same tactics, warning the public of airport delays, lax border security and thousands of teacher layoffs if the pending budget cuts take effect. He is trying to force Republicans to agree to ending tax breaks, mainly for wealthy individuals and corporations, that would raise as much as $580 billion.

“I’m not interested in playing a blame game,” Mr. Obama told shipyard workers in Newport News, Va., on Tuesday. “All I’m interested in is just solving problems. I want us to be able to look back five years from now, 10 years from now, and say we took care of our business and we put an end to some of these games that maybe, I guess, are entertaining for some but are hurting too many people.”

Said Republican strategist Whit Ayres, “The president is really good at campaigning and really bad at governing. So he’s doing what he’s good at.”

Mr. Schmidt said the president may have miscalculated that he can beat congressional Republicans with this strategy again because they conceded on tax increases two months ago.

“Republicans gave in on the higher tax rates on the revenue front, but that doesn’t mean a permanent acquiescence on these issues,” Mr. Schmidt said. “The president is beating Republicans in a public argument, but in fact Republicans are highly likely to retain the [House] majority because of demographics and where the competitive races are. If you’re lurching from crisis to crisis, people eventually get numb to it. There’s a ‘boy who cried wolf’ quality to it.”

The president’s effort to blame Republicans for the sequester is particularly galling to lawmakers who remember how it came about in the summer of 2011. Minority Leader Mitch McConnell, Kentucky Republican, gave a brief history of the episode Tuesday on the Senate floor.

“I was less than 100 yards from this very spot when Vice President Biden called me at my desk to lay it out,” Mr. McConnell recalled. “He explained the sequester in exquisite detail, and then, as has been reported, the administration stubbornly stuck by those details throughout the negotiations, refusing any effort by Republicans to adjust its design in any way.”

Since the fiscal cliff negotiations ended Jan. 1, Mr. McConnell’s aides say the president did not reach out to him on the sequesters until making a phone call last week. The two men didn’t have any personal encounters until Wednesday at the Capitol.

Mr. Obama’s motorcade arrived at the Capitol at 10:57 a.m. for the dedication of a statue of civil rights pioneer Rosa Parks. The ceremony began at 11:04 a.m. Somewhere in between, White House spokesman Jay Carney said, the president held a “brief meeting” on the budget cuts with Speaker John A. Boehner, Ohio Republican, and Mr. McConnell.

Pressed by reporters about the substance of a meeting that lasted less time than the average person’s morning shower, Mr. Carney conceded that the president mainly discussed his “anticipation” of a Friday meeting at the White House with congressional leaders.

That session, widely perceived as a photo opportunity, will be held on the same day that the budget cuts are to begin taking effect.

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