"Deep skepticism" refers to having a strong doubt or questioning attitude towards something, often with a lack of trust or belief in its truth or reliability. Full definition
But in a sign of the complexity and confusion surrounding the issue, neither the criticism nor the praise was perfectly partisan on Tuesday: Some Democrats hailed the idea as a needed dose of local mandate relief while some state Republicans reacted with deep skepticism about the plan's financial impact. (nytimes.com)
Many enthusiasts of Bitcoin and other cryptocurrencies are motivated by deep skepticism of the central banks that control the world's money supply. (jsmineset.com)