Between 80,051 and 94,115 immigration hearings were canceled during the five-week government shutdown, according to a new report. Those cases will be added to the system's record-high backlog, which as of Feb. 1 was reported to be 829,608.

Immigration experts warn that's only the beginning.

Relatively few new immigrations cases were recorded during the government shutdown, according to Tuesday's report from Syracuse University's TRAC. It added that "until new filings are recorded, any new [Department of Homeland Security] actions seeking removal orders aren't reflected in this backlog count."

According to the report, in 2018, between 20,000 and 25,000 new immigration cases were filed every month. But during the shutdown in January, that figure dropped to just under 5,600.

In other words, the immigration court backlog will be much higher once court officials are caught up.

"Unless there was a dramatic drop in arrests and removal actions initiated by immigration authorities during the shutdown period, there appear to be a sizable number of new filings yet to be recorded and reflected in the court's workload," according to the report.

The Department of Justice, which oversees the immigration court system, disputes TRAC's estimate of cancellations during the shutdown. An official at the agency told CBS News "our best estimate is that approximately 60,000 hearings were rescheduled because of the partial government shutdown."

Courts around the country are still catching up on the work they missed during the government shutdown. Hundreds of thousands of documents didn't get filed during the closure, leaving a mountain of work for court administrators to wade through. Even though the government reopened over three weeks ago, the Newark immigration court still hasn't caught up on filings, according to Alan Pollack, a Newark-based immigration attorney, who said that, "hundreds more cases have been rescheduled because the government did not have the time and resources to prepare."

In Los Angeles, the court had to authorize overtime pay for clerks who, as of Tuesday, were still wading through mail-in filings, said Ashley Tabaddor, the president of the National Association of Immigration Judges and a Los Angeles-based immigration judge herself.

"The administration failed to realize what a huge mess the shutdown was going to be for us," Tabaddor said in a telephone interview with CBS News on Tuesday. "They basically threw us into the water and said, 'sink or swim.'"

The vast majority of immigration cases have not yet been rescheduled, immigration attorneys told CBS News. None of Pollack's 12 cases that were canceled due to the shutdown have been put back on the calendar. Because of the backlog, he doesn't expect those cases to be rescheduled until 2020.

"The shutdown put a strain on an already overloaded system," Pollack said.