I find this story disturbing on many levels. Perhaps Miers couldn't think of anyone appropriate off the top of her head and thought that Leahy would like it if she said Earl Warren, but then caught herself when she realized that (rightly or wrongly) he was the poster boy for judicial activism. It would be odd to refer to Chief Justice Burger simply as "Warren." So perhaps the question was too difficult for her to answer without stumbling (of course, we all stumble in answering questions some time).
A second possibility is that she really does admire Earl Warren the most, but was unwilling to admit it to Leahy. That would seem a reasonable choice for a Democratic nominee, but not for a Republican. Further, to try to hide her choice from Leahy would show both cravenness and a lack of candor.
The third possibility is that she genuinely admires Chief Justice Warren Burger more than any other Justice that she could think of. If so, one wonders about the quality of Miers' judgment or whether she has read enough Supreme Court cases to form a reasonable opinion.
Burger was reputed to have done a good job running the federal court system, but is usually viewed as an indifferent or poor justice. I have never met anyone (conservative or liberal) who said that they really admired him, but I expect that many of his former clerks do.
2 hours ago