"Your children don't belong to you - they belong to everyone" --- that's the foundation and philosophy behind Common Core. Common Core is a component of the Race to the Top program which was initiated by this administration and immediately accepted by blue states. The most conservative states in the country want no part of it. To say the CCSS is a conservative idea with conservative backing is ignorant.
“If we must have an enemy at the head of Government, let it be one whom we can oppose, and for whom we are not responsible, who will not involve our party in the disgrace of his foolish and bad measures.”
- Alexander Hamilton. Spiritual father of #NeverTrump
As far as measuring students achievements, again that's a conservative idea as demonstrated by the current vogue in education - testing kids using standardized tests.
RTTP builds on bush*'s education program (if I remember correctly it was called Leave No Child Behind)
And it's no surprise that the right is rejecting their own ideas. It's not the first time. Conservatives also like to whine about zero-tolerance policies, individual mandates, state exchanges for insurance, and states rights (when it comes to health insurance - they want to eliminate the states powers to regulate insurance in order to enable insurers to sell across state lines)