I felt this way when I was very suicidal in a day-to-day sense. When I was a teenager, I was on a trip by canyons and kept having to talk myself into or out of running away and jumping. It felt like the opportunity was there but I was with other people, so extremely inappropriate. And it was this sudden urge to make a decision, now was the time and I had to either make the decision or not at all. My face felt hot and it was all I could think, I need to jump now, I really need to jump or it won't happen. I am still sort of confused if it was an intrusive thought or realizing it was one of the few opportunities I had to take my life without potential survival. I had many passing thoughts, but this felt more like an urge or a calling for that very second, that it needed to be now. Even though I hadn't planned for that opportunity, it was right there and I need to make an immediate decision before it passes. Obviously I decided against jumping, but it was an unprecedented sense of urgency. I've had other instances of holding a knife up to my stomach and trying to press in, sort of urgent but I also knew in the back of my mind that the success rate was low and that it would likely be too painful to go through with. I had a long-term plan of carbon monoxide but couldn't work up the courage until the day everyone was returning from their trip. It felt like a decision I put off or was maybe too reluctant to take until it was almost too late (even though the act itself felt urgent and necessary). It was a sort of last minute gamble that was pretty pathetic in comparison to its original plan, and the timeliness it took for everyone else to be out of the house for an extended period of time. In that case it felt almost opposite to urgency, where I was slow to act and fulfill plans even though I felt very ready and had prepped myself emotionally for a long time.
I only feel it now in response to ongoing harassment and violation. I was targeted by extremely sick people online and in daily life, their own careers made them more convincing and groups like anonymous helped in continuing to inflate the issue and basically taunt people into suicide (not a new thing for them). They have so many fake accounts where they'll essentially mimic your "personality," try to befriend you or demonstrate an issue — to convince you of anything really. Most grotesquely a form of care. When I see how bad it gets, it's worse than what some people might do privately (in most cases I wouldn't care to know). They make their harassment inescapeable, and then it feels like, again that immediacy, not so much in suicide but being the only way to put an end to what they (and bolder figures who show their face) do to people. I don't know that it's the same thing as being suicidal, but it's definitely an immediate sense of need.