They have only ever said that every position they are working on would offer a salary too low to compete even with what I currently made, let alone the larger amount I was seeking.
Yet at the same time, I have friends and colleagues who already are earning the higher level I am seeking, and who say it is a common amount to be earning in certain places.
My opinion is that recruiters focus a lot on whether it would be easy to get you hired. If your salary is high, few recruiters will bother because it means you are picky and you're looking to work at companies that are picky and so lots of times it doesn't work out.
Recruiters are a lot like crappy stock analysts. They are always looking for a story about something being undervalued, to hook someone on how they can get something great for an amazingly cheap price.
If you are justifiably expensive, most recruiters scatter like roaches. They can't sell things at their true value, and view it as wasting time even to try.
When things get more serious, I sometimes go over my history of compensation with them.
To me, it comes down to the question: does company X need me more than I need company X? For the right people with the right skills and the right experience, the "power" is with the potential employee.
The feedback I get from HR/recruiters is that my approach is rather unusual, but that they generally appreciate it since it is rather efficient.
Before I would speak to any of them on the phone, I'd get a soft confirmation via e-mail that they had a position that could meet my requirements.
The web page also had information about what areas I was willing to commute to.
I've used variants of this approach for more than 20 years, and it's working exceedingly well.