Generally, Republicans and conservative activists do a poor job of advocating their sensible and constitutionally necessary position. Matt Franck does outline a coherent strategy designed to change public opinion.
Unfortunately, those on the right tend to argue like lawyers, while Obama had (probably justified) contempt for his law school education (see his autobiography)--hence his emphasis on "empathy" as a judicial credential, which has attracted the ire of conservatives. If the right took to heart the Constitution's basis in the Declaration of Independence, they would sing a different song and interrupt the leftist appeal to the passions.
The Supreme Court is too important to be left to the lawyers--something Bush probably realized in his unfortunate initial pick of Harriet Miers. But he didn't have the skill (or the proper weapon) to make his point. The language of "judicial restraint" has no political cache and in fact is a secondary point. We want jurists who are zealous in their defense of the Constitution, while realizing the moderation essential to their office.