The key of security is around your comment extract a session attribute
-- how are you doing this? Are they sending you a query string param? Are they sending you credentials in the method headers?
To @Hogan's point, unless this is over HTTPS the answer is: "No, it is not secure. A man-in-the-middle (MITM) can get the password from your submission and simply re-use it to mask its own nefarious requests".
If the communication IS done over HTTPS, then you should be fine. Having a single hard-coded password is fine, but consider the case where the password gets compromised; now every single client/user/etc. has to change their code.
A better design is to issue clients a key they can send along with their requests that you can use to identify who they are and if a key gets compromise, re-issue a new one to that user/client/etc.
This assumes traffic is over HTTPS
If traffic is not, a lot of this breaks down and you need to look at things like HMAC's. I wrote this article on designing secure APIs -- it should give you a good introduction to how all this nightmare of security works.
If your eyes are rolling into the back of your head and you are thinking "My god, I just wanted a YES/NO", then my recommendation is:
- Require all traffic to be over HTTPS
- Issue individual passwords to each client so if one gets compromised, every single one isn't compromised.
- That should get you pretty far down the road.
Hope that help. This topic is super hairy and I know you didn't want a history lesson and just want to solve this question and move forward. Hope I gave you enough to do that.