So why are the two so often conflated?
It could be the "big lie" where a falsehood is said so often that the other side starts to believe it. But people are usually more sophisticated than that.
Another possibility is that we have lost perspective on the alternatives. We worry about reluctance to fire teachers but forget that private alternatives are not inexpensive. From Marginal Revolution:
A New York City charter school set to open in 2009 in Washington Heights will test one of the most fundamental questions in education: Whether significantly higher pay for teachers is the key to improving schools.
The school, which will run from fifth to eighth grades, is promising to pay teachers $125,000, plus a potential bonus based on schoolwide performance. That is nearly twice as much as the average New York City public school teacher earns, roughly two and a half times the national average teacher salary and higher than the base salary of all but the most senior teachers in the most generous districts nationwide.
However, this still doesn't explain the odd consensus of left and right as it seems improbable that many people are fighting for a serious increase in education costs.
Most likely, I suspect, the the current American focus on short term results. When we do annual ratings of employees, we do not consider issues of long term dedication -- we know people are simply going to move on anyway. Consider this report:
Among jobs started by workers when they were ages 38 to 42, 31 percent ended in less than a year, and 65 percent ended in fewer than 5 years.
Is it possible that, with 65% of middle aged workers holding a job for less than 5 years, that we have simply lost the sense of how to build long term loyalty and dedication?