Hi Andrew,
First off welcome to the forum!
With regards to the issue you have raised - the first observation is this: who is best placed to revise time and cost estimates for a project: someone new to the organisation who as a BA shouldn't be doing that anyway, or the established manager of that project? You have to wonder just why the decision has been taken to get you an outsider to do this...assuming the decision HAS been taken (has it been taken? Will you be presenting your estimates back to the steering group or will the manager?). Of course, as an outsider, if you do the estimates and they don't like them it is easier to shoot the messenger...
But you are where you are so what to do? If in doubt I would suggest you fall back on logic and honesty.
Follow the logic of determining what you need to do in order to be able to do the estimates sensibly (if you are acting as a BA and if you accept that as part of your BA role which it isn't normally). That means if you need to consult with the technicians and take their estimates then document that and communicate it. Please bear in mind that the technical aspects of the project are not the only factors to estimated: there is the whole business side of the implementation as well to plan in.
Be honest about what you can and can't do in terms of what skills you have, your role and resources. Analyse any issues from any shortfalls in any of that and also analyse any risks that arise - there are a load of templates for doing risk and issue anlaysis (can send you some if needed) but the key thing here is not the templates but the content: make the issues and risks relevant to the project. Example: a 'good' project risk is not something like "we may not have sufficient appropriate business resources to accurately estimate project implementation tasks" - in this case the risk is "the project may fail to meet cost and effort deadlines". Make it meaningful to the project and that means that just about all risks will be threats to any combinations of project cost, timescales, quality or scope.
Risk and issue analysis will be key in communicating to your audiences the adverse factors you face in approaching this assignment. From the information you have given it suggests that the project is not being managed effectively and there will only be so much you can do in an established off-target project, so help the project at least understand what state it is in by doing some rigourous risk and issue analysis with the added benefit that this should protect your position as well!
I hope this helps, let me know if you want the templates and likewise let me know if you wud like any help constructing a task list to revise the estimates and documenting the risks and issues.
Guy