Okay,
@Charris, speaking as someone who saw this from the front line...
My dh was medically retired in Feb 2009. His company decided it, not us. He also had LTD. His company actually was super nice and paid our COBRA for not just 18 months but longer than most...thru to Dec 2011, thank goodness. SSDI takes time to process. And almost everyone is denied the first time.
While we were waiting for his SSDI to kick in, his LTD covered our expenses (70% level which is higher than basic which is typically 50% but we paid to get covered at 70%. He finally got on SSDI in Oct 2010, we had to pay back the difference between SSDI and LTD. Yeah, we got all the back SSDI back to Feb 2009 but we owed it all to the company who handled the LTD. It wasn't until Feb 2011 that he was finally able to get on Medicare based on SSDI (there is a 2 year mandatory wait if disabled from the time of your disability as defined by SSDI).
When he filed for SSDI, I was already on it. (I was classified disabled in 1998, so my Medicare went into effect in 2000). I was very lucky in that I got mine first try. BUT I knew to have a lawyer handle dh's not me. I didn't want to get it in the middle of our marriage. We did end up paying the lawyer $6000 for all of it, paperwork, time, and even an appearance in front of a judge. See dh was denied not just once but twice so his had to go to a judge.
It's a long road...and most people are financially wiped out before getting there. Most companies have to provide COBRA but they make you pay for it. And COBRA is horridly expensive. Even if you start today, it will be June 2018 before you are allowed on Medicare (unless you turn 65 before that).