Role of the vice president The Constitution instructs that electoral votes must be sent to the president of the Senate – who is the sitting vice president of the United States – and that the Senate president must "open all the certificates" in the presence of both houses.
Results Once the votes have been "ascertained and counted in the manner and according to the rules ... provided" by the Act, "the results ... shall be delivered [by the tellers] to the president of the Senate." The Senate president "shall thereupon announce the state of the vote, which announcement shall be deemed a sufficient declaration of the persons, if any, elected President and Vice-President of the United States."

The president pro tempore of the United States Senate (often shortened to president pro tem) is the second-highest-ranking official of the United States Senate. Article One, Section Three of the United States Constitution provides that the vice president of the United States is the president of the Senate (despite not being a senator), and mandates that the Senate must choose a president pro tempore to act in the vice president's absence. Unlike the vice president, the president pro tempore is an elected member of the Senate, able to speak or vote on any issue. Selected by the Senate at large, the president pro tempore has enjoyed many privileges and some limited powers.

You need a President of the Senate to count the electoral votes. If Pence steps down, it seems the president pro tempore of the senate is Chuck Grassley.