The president of the Chicago Teachers Union on Wednesday called the latest proposal from the city on high school reopening “quite responsive” — but said staff members are staying home in protest anyway, because the sides still lack enough common ground.

“CTU is making very reasonable demands. … There has been progress but not adequate progress,” President Jesse Sharkey said at an early-morning news conference.

The sides are stuck on what he called “a fairly limited set of issues,” including vaccine access for students and their families and accommodations for teachers who want to continue to work remotely because of medical conditions.

Despite rising COVID-19 numbers in the city, local leaders have so far stuck by their Monday target date for reopening Chicago Public Schools’ high schools for the first time since March 2020. Officials have stressed the importance of resuming in-person learning and the limitation of remote learning and also that their safety plans are robust.

Cases of COVID-19 linked to elementary buildings that have been open for several weeks — but with only a fraction of eligible students, whose families chose for them to return — appear to be relatively low, according to CPS data. Last week, CPS reported 40 adult cases and 18 student cases among the tens of thousands of students and staff members who have resumed in-person classes.

But the teachers union has also cited the particular scheduling challenges for high schools, where students typically are in different groupings with different teachers several times a day. That complicates the adoption of the “pods” model in use in elementary buildings, where students remain with the same group of children throughout the day to limit their number of contacts and help with social distancing.

CTU chief of staff Jennifer Johnson said it’s important to consider the characteristics of individual buildings, like whether they have windows that open, the size of classrooms and adequate spaces for staff.

“We really should be erring on the side of having less people in the building … so there is less contact,” Johnson said.

She echoed comments of CTU lawyer Thad Goodchild, who said CPS’ approach to in-person learning has been, “unfortunately, trying to get as many people back in school buildings as … fast as possible.”

Rather, he said, “stability and safety are what parents want most. … That is what is going to build confidence.”

Eden McCauslin, a teacher at Taft High School, noted that the school had something of a dry run for reopening Tuesday when about 900 students came to the school to take the SAT exam.

At the entrance she staffed, it took nearly two hours to get all of the students into the buildings, and she said the day left staff with “a lot of concerns” about the reopening. She said about 2,000 students have opted in to in-person classes between Taft’s two campuses.

Another big union push is getting the city to open up vaccines to anyone 16 and older, as is the case now in the rest of Illinois, and providing access to those students and their families at the four CPS vaccination sites now in use for staff members.

According to the union, the city’s offer so far is only to provide vaccines for a small number of 18-year-olds who are CPS employees.

Despite the continued impasse, union representatives suggested a resolution could be near from the latest CPS proposal. Sharkey said it came too late Tuesday for him to call another meeting for union consideration.

It’s unclear if a resolution will come in time for Monday’s target high school return.

CPS parents who support a broader return to in-person learning are speaking out against CTU’s actions, saying the union is “moving the goalposts once again.” A group calling itself coalition of parents from around the city held a protest outside of CTU headquarters Tuesday evening.

“As parents, we are disheartened, seeing the pain that (closed schools) is causing our young adults, who have had the hopes of returning to in person learning threatened again by an overzealous Union, functioning more as a PAC than an advocate for the children they serve. CTU ‘proudly’ displays ‘We will Win!’ on the Facebook page of Jesse Sharkey, a slogan that reflects the union’s determination to win at any cost…particularly that of the children,” the coalition said in a news release.