“JPMorgan is one of the best managed banks there is,” he said while taping an interview on the ABC program “The View” to be broadcast Tuesday. “Jamie Dimon, the head of it, is one of the smartest bankers we got, and they still lost $2 billion and counting. We don’t know all the details. It’s going to be investigated, but this is why we passed Wall Street reform.”

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“You could have a bank that isn’t as strong, isn’t as profitable managing those same bets and we might have had to step in,” Mr. Obama added.

At Barnard, the president referred only obliquely to Wall Street, saying, “Some folks in the financial world have not exactly been model corporate citizens.” Instead, he kept the focus squarely on women’s issues.

Squabbles over federal financing of Planned Parenthood and coverage of contraceptive services have emboldened Democrats who believe they can exploit a gender gap in the November election. Mr. Obama tried to leap into that gap on Monday, with a speech that drew heavily on his childhood, reared by a single mother and an ambitious but frustrated grandmother; his marriage to a strong-willed professional woman; his high hopes for his two daughters; even his cabinet, filled with accomplished women, from Secretary of State Hillary Rodham Clinton to Secretary of Labor Hilda L. Solis.

At one point, after assuring the crowd that “all of you will help lead the way,” Mr. Obama cheerfully acknowledged he was pandering. “I recognize that’s a cheap applause line when you’re giving a commencement at Barnard,” he said.

Much of Mr. Obama’s address offered the bromides common to such speeches. At times, he recited standard policy messages on health care, education and alternative energy sources. At other times, he mixed fatherly advice with thoughts of his own daughters and reminiscences of his younger days.

Yet the timing gave it an unmistakable political subtext. Hours before Mr. Obama spoke, the Romney campaign and the Republican National Committee circulated reminders via Twitter and e-mail about how tough the job market has been for college graduates in the past few years.

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For the last several months, Democrats have tried to leverage women’s issues against Republicans, attacking them for targeting Planned Parenthood, for resisting Mr. Obama’s contraception mandate, and over the Paycheck Fairness Act, which Senate Republicans have rejected.

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In the latest skirmish, the parties are battling over competing versions of the Violence Against Women Act, a measure that usually sails through Congress without controversy.

The Republican-controlled House this week is set to vote on a basic extension of the act, which aids local law enforcement agencies and finances shelters and other programs for battered women. That has set up a showdown with Senate Democrats, who have already passed legislation that would expand efforts to reach Indian tribes and include same-sex couples in programs for domestic violence.

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Mr. Obama cited the travails of Lilly Ledbetter, for whom his administration’s equal pay law is named, as well as pioneering legislation pushed by two senators, Barbara A. Mikulski, Democrat of Maryland, and Olympia J. Snowe, Republican of Maine.

Still, his tone was upbeat and he was on familiar ground. Mr. Obama’s sister, Maya Soetoro-Ng, graduated from Barnard in 1993. Ten years earlier, he graduated from Columbia. (“I know there can be a little sibling rivalry here,” he said.)

Mr. Obama later spoke at a fund-raiser, where one of the hosts, Ricky Martin, the openly gay pop star, said he admired the president for his courage in endorsing same-sex marriage.

For his part, Mr. Obama said: “I want everyone treated fairly in this country. We have never gone wrong when we’ve extended rights and responsibilities to everybody. That doesn’t weaken families; that strengthens families.”