There is a way to be a leader without it, but not for long.
You have to have a holy stubbornness that disallows resignation. It has to offend you to let up on what is right. You can feel the cramps under your ribs, but you have to bypass your ribs and just start communicating to your legs directly. Your legs will ask if you've checked in with your ribs, but you will tell your legs to keep moving and to make like your ribs don't exist for now. Call it "mind over matter" if you want, but whatever you call it, a leader must possess this quality.
I know it sounds like I'm promoting a quasi-denial that can cause you to live outside reality, but this is not my submission. All I'm saying is that a leader must be able to divide motions and emotions for successful long-distance running. If you concentrate too much on the one nagging issue, the "issues" stack and form a pile-on that eventually cancels you out completely, neutralizing your vision and passion. But I'm straying a tad.
Back to tenacity.
This virtue is essential to survival. In a world of "dripping faucets" and "nagging injuries", you simply have to press through difficulty with "mental tricks". You have to tell yourself to keep going in terms your heart can comprehend. Things like: "Don't take that personally." or "You are a good guy despite what you are feeling right now." or "Take that situation with a grain of salt." or "Just keep pressing on until that date night with your wife tonight." or "It could be worse." or "It will be worth it all when we see Jesus" (ok, that's a hymn that just came to my head from my childhood) All this to say, talking yourself through funks is essential to going the distance.
After you face daunting odds and digs of opposition in your efforts or initiatives, you have to roll with the punches, pick yourself off the ground, dust yourself off (this is the self-talk aspect I'm talking about) and get to where you were going in the first place.
Tenacity is certainly more than what I've shared, but this is, to me, a huge element of gritting your teeth, setting your jaw, and moving forward.
And if leadership is anything, it's moving forward.