Self-supervised sentence representation learning is the task of constructing an embedding space for sentences without relying on human annotation efforts. One straightforward approach is to finetune a pretrained language model (PLM) with a representation learning method such as contrastive learning. While this approach achieves impressive performance on larger PLMs, the performance rapidly degrades as the number of parameters decreases. In this paper, we propose a framework called Self-supervised Cross-View Training (SCT) to narrow the performance gap between large and small PLMs. To evaluate the effectiveness of SCT, we compare it to 5 baseline and state-of-the-art competitors on seven Semantic Textual Similarity (STS) benchmarks using 5 PLMs with the number of parameters ranging from 4M to 340M. The experimental results show that STC outperforms the competitors for PLMs with less than 100M parameters in 18 of 21 cases.