In his response, Mr. Buttigieg emphasized that Mr. Trump’s approach violated Mexican sovereignty and the need for Mexican cooperation and approval in any military response.

“There is a scenario where we could have security cooperation as we do with countries around the world,” Mr. Buttigieg said. “Now, I would only order American troops into conflict if there were no other choice, if American lives were on the line and if this was necessary to meet treaty obligations. But we could absolutely be in some kind of partnership role, if and only if it welcomed by our partner south of the border.”

What they’re talking about

Senator Elizabeth Warren claimed that her 2 percent wealth tax on households worth more than $50 million would pay for a sweeping expansion of the nation’s social safety net, providing free child care and college tuition.

What Ms. Warren said:

“We can put $800 billion new federal dollars into all of our public schools. We can make college tuition-free for every kid. We can put $50 billion into historically black colleges and universities. And we can cancel student loan debt for 95 percent of the folks who have got it.”

The revenue that Ms. Warren would raise from her tax proposal is a subject of intense debate and it is not clear that her wealth tax could pay for the plans she listed. According to a New York Times analysis, the total cost of Ms. Warren’s plans for universal child care, increased spending on public schools, student debt cancellation and free college would be about $2.9 trillion over a decade. The two Berkeley economists advising her campaign, Emmanuel Saez and Gabriel Zucman, estimate that her wealth tax would generate $2.75 trillion over that period of time. If that is correct, then Ms. Warren would be close to being able to pay for those proposals. (Ms. Warren has recently revised her wealth tax proposal, and Mr. Saez and Mr. Zucman have refined their calculations but the general conclusions are the same.)

But other economists disagree, arguing that a wealth tax would spur waves of new loopholes and tax evasion efforts. Lawrence H. Summers, a Treasury secretary under President Bill Clinton, and Natasha Sarin, a law and finance professor at the University of Pennsylvania, estimated that Ms. Warren’s wealth tax would raise just 40 percent of what her campaign claims.