I think the effort is an exercise in futility.
As the article says...
If Obama were to nominate Rice, it would be up to the Senate to confirm her, not the House. But the House Republican letter mirrors some of the Senate Republican criticism of Rice that has emerged.
Sens. John McCain (R-Ariz.) and Lindsey Graham (R-S.C.) said they would work to block the nomination in the Senate. But hey, they’ll have to avoid having a recess because Obama WILL make the recess appointment ( he already did that once ).
Elections have consequences.