I'm talking about traditional conservative Republicans in the Bush mold, not conservative Republicans in general.

Tom DeLay was right wing. However, President Bush was conservative on quite a number of issues while being moderate on others. Comprehensive immigration reform efforts during Bush's time were not right wing. President George HW Bush also raised taxes during his time.

Also, regarding the Sununus, they are not right wingers. Per On the Issues, NH Governor Chris Sununu and his brother, former US Senator John Sununu.

Chris Sununu - Moderate conservative

ontheissues.org/Chris_S…

John Sununu - Libertarian conservative

ontheissues.org/House/J…