Rapid and cost-effective DNA sequencing at the single nucleotide level might be achieved by measuring a transverse electronic current as single-stranded DNA is pulled through a nanometer-sized pore. In order to enhance the electronic coupling between the nucleotides and the electrodes and hence the current signals, we employ a pair of single-walled close-ended (6,6) carbon nanotubes (CNTs) as electrodes. We then investigate the electron transport properties of nucleotides sandwiched between such electrodes by using first-principles quantum transport theory. In particular, we consider the extreme case where the separation between the electrodes is the smallest possible that still allows the DNA translocation. The benzene-like ring at the end cap of the CNT can strongly couple with the nucleobases and therefore it can both reduce conformational fluctuations and significantly improve the conductance. As such, when the electrodes are closely spaced, the nucleobases can pass through only with their base plane parallel to the plane of CNT end caps. The optimal molecular configurations, at which the nucleotides strongly couple to the CNTs, and which yield the largest transmission, are first identified. These correspond approximately to the lowest energy configurations. Then the electronic structures and the electron transport of these optimal configurations are analyzed. The typical tunneling currents are of the order of 50 nA for voltages up to 1 V. At higher bias, where resonant transport through the molecular states is possible, the current is of the order of several μA. Below 1 V, the currents associated to the different nucleotides are consistently distinguishable, with adenine having the largest current, guanine the second largest, cytosine the third and, finally, thymine the smallest. We further calculate the transmission coefficient profiles as the nucleotides are dragged along the DNA translocation path and investigate the effects of configurational variations. Based on these results, we propose a DNA sequencing protocol combining three possible data analysis strategies.