Christine A. Reuther, the Delaware County councilwoman who wrote the grant proposal for her county, said that the funding helped the county train poll workers and acquire drop boxes, some of which were dispatched to majority Republican municipalities.

“I have no idea why it is a bad thing, let alone unconstitutional, for Delaware County to accept a grant to improve safe and secure access to the polls for all of its registered voters,” she said, calling the lawsuit a “time-consuming, resource-wasting effort.”

In a statement, the Center for Tech and Civic Life called the lawsuits “baseless,” and said the group was nonpartisan, working with Democrats, Republicans and nonpartisan officials.

Conservatives have raised concerns about the political backgrounds of the center’s co-founders, who the lawsuits note had worked together at a Democratic Party-aligned organizing group, and of Mr. Becker. He had briefly worked for the liberal group People for the American