Support for President Trump’s border wall hit a record high in a new Quinnipiac University poll Tuesday, but a majority of Americans still oppose the project, saying it’s a waste that isn’t needed to improve border security.

The poll found 43 percent do support the wall, but 54 percent oppose it and say it won’t help secure the southern boundary.

And the survey dealt a major blow to liberal activists’ hopes of impeaching Mr. Trump, with just 12 percent saying that should be Democrats’ top priority as they take the reins of the House in the new year.

Even among Democrats, just 19 percent said they want to see their party prioritize that over everything else.

Asked about a whole series of priorities, health care topped Democrats’ list with 31 percent saying they want that to be the focus, followed by the environment.

Among Republicans, immigration was the runaway winner, with 52 percent saying they wanted to see action.

The findings come as Mr. Trump is engaged in a shutdown showdown with congressional Democrats, seeking to win at least $5 billion in new money to continue expanding the fencing along the border.

Mr. Trump has eagerly cheered a shutdown, while members of Congress — both Democrats and Republicans — are generally unenthusiastic about a nasty disruption during the holiday season.

The Quinnipiac poll indicated that more Americans will blame the president and his party than Democrats, by 51 percent to 37 percent.

“A blunt holiday greeting card for President Donald Trump: Don’t build a border wall and don’t shut down the government to try to get it done,” said Tim Malloy, assistant director of the poll.

Support for the wall was just 33 percent in Quinnipiac’s polling in early 2017, as Mr. Trump took the reins of government after a long campaign of promising a border barrier.

It reached 40 percent in April, as an earlier migrant caravan stormed the U.S., then dipped over the summer. But with new caravans sitting on the border again testing the U.S. boundary, support for the wall rose to 43 percent in the latest survey.