Secretary of Homeland Security John Kelly told a Senate committee hearing on Wednesday that President Donald Trump’s much-touted border wall is “unlikely” to stretch from “sea to shining sea.”

“It’s unlikely that we will build wall or a physical barrier from sea to shining sea,” Kelly testified. “We’re not going to build a wall where it doesn’t make sense. But we’ll do something across the southwest border.”

Kelly also said that he could not predict how much the wall would cost. He also said he did not how high it would be, what color it would be, and whether “it will have solar panels on it.”

Kelly, a former Marine general, made the remarks while being questioned by Sen. Ron Johnson, R-Wisconsin, during a Homeland Security committee hearing held on border security. His comments provoked a derisive response from Sen. Claire McCaskill, D-Missouri, the ranking Democrat on the committee, who said it’s “embarrassing” that Mr. Trump does not realize the wall could be that long.

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“It’s embarrassing,” McCaskill said. “It’s not going to happen. Everybody in Congress knows it’s not going to happen.... It appears the only person who won’t say it out loud is the president.”

Mr. Trump’s oft-stated promise to build a “big, beautiful” wall was a cornerstone of his campaign pitch. He also promised repeatedly that the wall would be paid for by Mexico, although the White House has since requested that some money for the wall be included in the upcoming budget currently being negotiated by Congress. An internal DHS report presented to Kelly in February indicated that the wall would cost more than $21 billion.

For its part, the Mexican government has said that it will not pay for the wall, a point McCaskill reiterated during her questioning. “Mexico is not going to pay for it,” she said.

Mr. Trump has insisted a physical barrier is necessary to stop the inflow of undocumented immigrants and drugs from the southern border, which stretches some 2,200 miles. Kelly defended Mr. Trump’s assertion, saying that it’s clear existing physical barriers along the border work well.

“The barriers work,” Kelly said. “Technology also works.”