That is strictly a conservative fantasy. It's a false premise demonstrated by the fact the liberals push education and conservatives only have contempt for education. If you were honest, you would admit that.
If liberals support education why have they not set up a program where everyone who receives welfare gets to go to the college of their choice? Why did they oppose the Welfare to Work program under Clinton?
If you view all questions of education by these two razors, it will illuminate the supposed leftist support for education:
"Will the proposed bill have the effect of keeping or adding to more dues paying union members?"
"Will the proposed bill be a handout to some group that may become a new suckler at the teat of the government?" (see Pell grant and student loans in general)
If the answer is no to these questions, then the leftists are not for "that kind of support for education."
A prime example is school choice, the Dems are against it even though their constituency (blacks) are for it. Even though this will tend to have the effect of lifting this group out of poverty over time, the Dems oppose it. Why? Because of what it will do to teachers.
The employee trumps the child.