I would like to know if there is a way to prevent an html page with jQuery or javascript to be modified by the user to change its behavior.
A user can modify it usin
As others have already said, it isn't possible to control what the end user does with data you've sent them.
It may be possible to detect the console object that Firebug and others use, but what can your site do with that information once you've got it? You can't disable firebug or prevent it from being used, or even know whether it has been used.
The bottom line is that once the web page and javscript code have been sent to the browser, it is out of your control.
The closest you can get to what you want is to move some of your code out of Javascript and to the server, where it will be untouchable by the user. However you'll still have to have some client-side code, which will still be at the mercy of malicious users.
The other alternative is to move to Flash or something similar, where the end user doesn't have direct access to the code or the object model. This has it's own downsides though, and you'd be bucking the trend, which is to move away from Flash toward HTML5 and Javascript.