ABC News' Matt Jaffe and Alex Perez report:

The Chicago teachers' strike will stretch into a third day Wednesday after negotiators failed to reach a deal yet again this evening.

After another long day of talks, David Vitale, the president of the Chicago Board of Education, told reporters that his side had presented the teachers' union with an updated proposal tonight and he would not return to the negotiating table until the teachers responded with a written proposal of their own.

"It is time for us to get serious," Vitale said.

While Vitale said the two sides had reached agreements on various issues, a key sticking point remained a new system for teacher evaluations.

"I would not say that we came to an agreement on the fundamentals of all that," Vitale said.

Minutes later, Jesse Sharkey, the vice president of the Chicago teachers union, came to the cameras to explain that, in his view, his side had essentially been given an ultimatum.

"We do feel like it's sort of an attempt to throw down the gauntlet, and that's an unwelcome development," Sharkey said. "At the end of the day, they basically dug in their heels."

Sharkey said the main topic of discussion today was the evaluations. He expressed frustration that the latest offer from the city would, according to him, leave 28 percent of Chicago teachers in jeopardy of losing their jobs within the next two years.

"The idea that 28 percent of our teachers could be fired due to poor performance is really an insult to the profession," he said.

Despite the back-and-forth between Vitale and Sharkey tonight, staffers from both sides are scheduled to meet again Wednesday at 11 a.m. CT. In the meantime, the Windy City's first teachers' strike in more than two decades will now extend into a third day.