The base would have been fired up with Alito anytime, anyway.
From a White House perspective the Miers nomination made Bush look weak;
(1)she was a weak candidate in terms of background,
(2)not supported by his base
(3)no big objections from too many Dims
so
(a) her nomination initially looked like he was responding to Dim demands that he not name someone "controversial",
(b)then it simply looked like a weak nominee,
(c)and then pulling her out was sold by the Dims as "caving in to the radical right".
Altogether, it was a flawed and bound to fail nomination and it helped depress the public's belief that he was doing a good job.
If anyone has been wondering where Bush's "liberal" positions might originate, they need look no further than Andrew Card - associate of Sununu, backers of Souter.