WEST LAFAYETTE, Ind. — Outside an engineering building here, Lauren Johnson offered pandemic-safety gear to students hustling to the first classes of the fall term. But no one who had passed her so far on this blue-sky morning needed a "Protect Purdue" mask.

“I would say a majority of students are abiding by the regulations right now,” Johnson said Monday. “It’s not a perfect world, and we’re going to have some people not follow the rules.”

The 22-year-old senior from West Lafayette belongs to a squadron of Purdue University safety “ambassadors” paid $9.50 an hour to promote measures the public institution is taking to protect its campus from the novel coronavirus.

Purdue has become a national poster school for the push to bring students to campus and teach in person despite the public health crisis — a push that in many other places has failed or is in deep jeopardy. The wave of fall reopenings, now accelerating, has exposed the fragility of plans that once seemed solid.

The University of Notre Dame put in-person teaching on a two-week hiatus after virus cases surged. Butler University, in Indianapolis, flipped to remote instruction for two weeks as it opened Monday after noticing what it called “a lack of compliance” with health guidelines among “a relatively small proportion of our students.”

The University of North Carolina at Chapel Hill scrapped face-to-face classes entirely for undergraduates on Aug. 17, a week after classes began. Coronavirus cases connected to UNC-Chapel Hill rose sharply in the past week as more than 30 percent of those tested were found to have the virus.

Ohio State University officials recently disclosed they have issued more than 200 “interim suspensions” of students for potential violations of health and safety rules related to the pandemic. The University of Alabama System this week is reporting 566 coronavirus cases since Aug. 19 among students, faculty members and staffers. That includes 531 on the flagship campus in Tuscaloosa, where in-person classes are underway.

On Tuesday, the University of Virginia started online with hopes of switching to in-person classes after Labor Day.

Much is riding on whether Purdue’s plans to teach in person remain on track or succumb to the virus.

If Purdue is forced to pivot to an online-only semester, other public universities could face pressure to follow suit, said Christopher R. Marsicano, an assistant professor of the practice of higher education at Davidson College in North Carolina who is tracking pandemic responses.

Marsicano’s analysis of 100 major public universities shows 47 are opening primarily or fully online. Others have hybrid teaching plans or are still deciding what to do. Purdue is one of just 27 opening primarily in person.

“The question now is, ‘Will Purdue last?’ ” Marsicano said.

Soon after the virus upended the spring semester nationwide, Purdue President Mitchell E. Daniels Jr. declared the university had a duty to provide its 45,000 students the chance to come here in the fall to learn.

“To tell them, ‘Sorry, we are too incompetent or too fearful to figure out how to protect your elders, so you have to disrupt your education,’ would be a gross disservice to them and a default of our responsibility,” Daniels, a Republican former governor of Indiana, wrote in May.

In June, he boasted to a Senate committee that the university was acquiring more than a mile of plexiglass to protect faculty and staff members from airborne transmission of the virus. But this month Daniels warned students that opening the university “wasn’t an easy call,” and he cautioned that the university could shift course if conditions became untenable.

On Monday, Purdue declined to make Daniels available for an interview. “We don’t feel we are in the spotlight as we are one of many schools returning to campus,” Purdue spokesman Tim Doty wrote in an email.

The university has required extensive viral testing of students, and like others it is cracking down on risky behavior. Last week, 36 students were suspended for failing to wear masks and keep adequate distance from others at an off-campus party. An online dashboard showed 35 students and six employees tested positive for the coronavirus, out of 1,661 tests given from Aug. 16 through Saturday. The positivity rate was about 2.5 percent.

Faculty members are divided. “To be clear, I have colleagues who are looking forward to face-to-face teaching. But I would say they’re in a minority,” said Alice Pawley, an associate professor of engineering education who leads the campus chapter of the American Association of University Professors.

The university said medically vulnerable employees are allowed to work remotely if needed. “We did not force anyone to teach in person,” Doty said.

But Pawley said she has heard of faculty members who felt pressured to teach face-to-face even though they did not want to. Lecturing behind plexiglass, she said, is not the solution. “It should be about student learning,” she said, “and not about the optics of teaching face-to-face no matter what.”

Patrick J. Wolfe, dean of science and professor of statistics and computer science, said faculty and staff members he works with are upbeat. “My sense is that the majority of folks are pretty enthusiastic about trying to manage our way through this in a way that’s ultimately good for the students and takes care of people’s safety,” he said.

On the first day, students ambled around a campus that felt sparsely populated. They tried to keep distant from one another, and no one could be seen without a mask. Some sat at tables outside a Starbucks with headphones on and laptops open, Zooming into courses rather than walking into lecture halls. Others lounged on the grass and balanced computers on their chests or stomachs.

As the Purdue Bell Tower chimed, a class of about 20 students met on the lawn of the Engineering Mall. Associate professor Mireille “Mimi” Boutin struggled with an iPad to get a handful of virtual students dialed into the electrical and computer engineering course via Zoom. “It was a disaster,” she said. Some students couldn’t connect, so she would have to find time this week to give the same introductory lecture again. “I’ll have to teach on Sunday. I’ll have to teach at night.”

Boutin said she cannot meet in her classroom, because of space restrictions. That morning, she found out a lab for the course will be online. “We’re told: ‘This is the situation. Deal with it,’ ” Boutin said. “But when it comes down to making things work?” Her voice trailed off.

Toward the back of the group, Eric Lutz, 21, a junior from Ravenna, Mich., strained to hear. “I’d much prefer to be in the classroom, but if there’s not enough space in the classroom, I guess you can’t be in there anyway,” he said.

Between classes, Megan Balog, 22, a senior from Virginia’s Loudoun County, sat in the shade of a white tent not far from the Neil Armstrong Hall of Engineering. Balog said the classrooms she has seen appear to be “super clean inside” and “way less condensed.” There were lots of hand sanitizer stations and buckets of cleaning wipes.

Balog said classmates are taking extra care with safety. “To us, labs are super important,” she said. “So we need to be allowed to go to labs, so we’re going to follow the rules.”

Off campus, David Sanders, an associate professor of biological sciences, was preparing to teach a course on the coronavirus to 50 students via Zoom. He summed up the faculty’s mood: “Frustration. Confusion.”

Sanders said he has noticed a change in tone from leadership as the university has sought to curb large-scale parties that could jeopardize the reopening.

“We’ll see whether the coercion is effective or not,” he said. “It is certainly inconsistent with what Daniels has been saying all summer, which is, ‘Everything is going to go fine because we’re not going to need to use coercion because the students are going to come here and be uniquely saintly.’ ”

Anderson reported from Washington.