Axios has a good article about the week ahead for Biden and the Democratic nomination. Here's the money quote:
"The sh*t is going to hit the fan on Monday, when Congress returns," a House Democrat told us. "People are scared about their own races. But they're also worried about the country, and about democracy."
The article describes a lot of the behind-the-curtain maneuvering to get Biden to exit the race.
Bottom line: Democrats are going to work to create a consensus pushing Biden to drop out of the race by this Friday (July 12). They want a resolution before the GOP convention the following week (July 15-18) and the Olympics (July 26-August 11). On the other side, Biden and staff are hoping a few big events this week, including a NATO meeting, will calm the storm. They're betting the folks opposing him won't want to set the party on fire just to get him out of the race.
I expect to see Democrats provide a few requirements that Biden must meet to retain the support of the party. I would expect taking a battery of cognitive and memory tests (and releasing the results) might be one. They may demand that he hold town halls and other unscripted events before the convention. If the White House refuses, it will give wavering Democrats political cover to come out and demand Biden step aside.
I personally think the best time for Biden to resign is shortly after the GOP convention. The Republicans will spend four days not knowing who their target will be, which will make the event less effective.