The issue behind the question is whether there is still a possibility of a better offer than the loan modification that is being offered to you. However, there is no way to tell whether a particular offer is the best one unless some comparisons are made. To compare, you will have to ask around and check the kinds of interest rates and terms that are being offered to others. If you find that the offer is very close to what others are getting, then there is no reason not to accept the loan modification offer.
There is also the possibility that your bank may no longer make another offer if you do not accept it. On the other hand, you may still get a better offer if you counter the offer. It is really difficult to predict what the lender would do but if you already know that the terms are close to what is being given to most borrowers, negotiating for better terms may turn out to be futile.
However, if you think that the terms still do not fit your budget, there is nothing to lose if you ask for a better offer. If the payments are not affordable, there is no sense in accepting a losing situation. You will just find yourself in default and risk foreclosure.
And if you counter the lender’s offer, there is the possibility that the bank may offer something better. If not, it is time to look for other alternatives to avoid foreclosure.