In the NRO editorial "Withdraw Myers", they suggest that Bush finds someone a bit more qualified to head Immigration and Customs Enforcement than the current pick of Julia Myers since she has no immigration experience:

[ICE is] a vast bureau with more than 20,000 employees and a budget of $4 billion. As head of ICE, Myers would be in charge of detaining and removing illegal aliens; investigating alien smuggling, illegal arms exports, and money laundering; fining the employers of illegal aliens (well, actually they don’t bother with that any more); plus many, many other responsibilities. She would be the officer chiefly responsible for protecting the nation against terrorist threats once they have succeeded in infiltrating our borders, which are guarded by a different bureaucracy. Her most relevant previous experience was managing only 170 employees and a $25 million budget while at the Commerce department...

...The response of House Republicans to any talk of new immigration programs has been "Enforcement First." Replacing Myers with a more suitable candidate would signal that the White House takes these concerns seriously. Obstinately sticking to the nomination would send the opposite message.

I seriously doubt that immigration enforcement or competence are anywhere near the top of the administration's priorities. If they withdraw her nomination, the only reason will be because of the heat they've received.

Previously: "More on Bush's pick to head Immigration and Customs Enforcement".

UPDATE: I changed the title because the Miami Herald has joined in with "An unqualified nominee for a top job".