Hotline claims to know how this Miers decision worked:

"The tipping point came within the past several days. GOP Senators privately communicated to WH CoS Andy Card that unless they had access to hard evidence that Miers was conversant in constitutional issues, there was no way she would be confirmed. Her performance in private meetings was weak, at best, these senators told Card. Throughout the day yesterday, says a senior Senate aide, there were "conversations throughout the day at the staff level." Late yesterday, Senate Maj. Leader Bill Frist (R-TN) called Card and told him in no uncertain terms that Miers would probably not be confirmed. An aide: "He provided frank assessment of situation in the Senate. [The] lay of land on committee." After that call, according to White House sources, Bush and Card met privately with Miers, and they decided jointly that preserving WH privilege on documents was too important a principle to risk. Miers officially informed Bush at 8:30 pm ET. As late as 8 p.m., one White House aide said the WH counsel’s office was rushing to finish a revision to the Senate Judiciary Committee questionnaire. (It arrived after 11:00 pm ET). Word began to spread through conservative Washington last night. The White House office of political affairs notified allies at about 8:30 a.m ET this morning but swore them to secrecy until the White House released the President’s statement.

Also note this valuable chronology from the Wall Street Journal.