Why now? what has changed? The Dati Leumi leadership have been very opposed to a deal until now, and calling support for a "responsible" deal doesnt really change anything as all along they have said they would support a deal but only a responsible one (question is always what qualifies as responsible). Now? There are not even any talks or discussions of a deal on the table. Sinwar has been incommunicado for a long time and only yesterday did they say he finally has been in touch with Qatar and is really alive. Why now? What is this letter meant to accomplish?

One option is that it is just meant as an attempt to improve their own public image. The DL community has been painted as being against any deal, maybe they dont care about the hostages, and the like. A letter in support of a deal, especially when it costs nothing as no deal is on the table, can go a long way in repainting the image of the community. See - we are in favor of a deal, we do care about the hostages.

The other option, in my mind, is that there is, perhaps, something going on behind the scenes that the public has not been made aware of. Perhaps talks, or the start of talks, and a possible deal approaching. This letter, according to my theory, is meant to start paving the way and preparing the public for a deal that might be presented soon. I would not be surprised if Netanyahu is ready to make a deal for the hostages and this letter is at his bequest (in his usual roundabout ways) to start preparing the ground. Saar recently joined the government so even if Ben Gvir would remain opposed it could still pass a vote without him. 

Just a theory, dont get your hopes up just yet, but let's see where this goes, and hopefully we will see the hostages home soon!