The local inns are bursting at the seams and may not be able to accommodate [The underlined phrase means]:

Explanation

If a place is bursting at the seams, it has a very large number of people or things in it (to be very full or crowded).Example Sentences:Now that they have six children, their little house is bursting at the seams.When the whole family comes home, the house is bursting at the seams.