The next-generation of all-sky EAS detector will be able to lower the threshold below the TeV region and will provide a huge data flux, due to the large detecting area and the high duty cycle. In this paper we discuss in detail the possibility of using this detector in order to study the cosmic ray spectrum in the TeV region. The peculiarities of this class of next-generation detectors will make it possible to study the energy profile in the region where direct measurements are available with a large statistical significance. In such a way the measurement obtained by an indirect technique can be fully overlapped with direct measurement data, in order not only to study the cosmic ray spectrum but also to investigate the reliability of the full Monte Carlo simulation process. The sensitivity of such a measurement is also discussed and the data taking time required for a significative measurement is estimated. A standard chi-square fit and a Bayesian unfolding procedure are applied in order to obtain a measurement of the spectral index of the incoming primaries.