I would ask the hotel what they take as cover for incidentals for this long a stay, then you know where you stand.

I would ask your CC company for a limit increase in any case, explaining to them you have a new job etc.

I was most annoyed a couple of weeks ago where I was asked to show my credit card on check in (which I am quite used to doing) and instead of the usual couple of hundred dollars hold on my credit card, put through a pre-authorization for the entire stay, plus $200 per night incidental coverage - as it was an 8 night stay, I was not expecting $1600 of incidentals to be held! So best to check.