New Deal for New Americans Act of 2021 This bill provides assistance to immigrants and addresses issues related to naturalization. The bill establishes the National Office of New Americans to (1) welcome and support immigrants, (2) promote and support immigrant integration, and (3) promote the pursuit of U.S. citizenship among immigrants. The bill also establishes grant programs for eligible entities that provide (1) legal services for immigrants, (2) English language education that focuses on integrating students into society, and (3) workforce development training that supports the economic integration of immigrants. The bill also reauthorizes the Citizenship and Integration Grant Program within U.S. Citizenship and Immigration Services (USCIS). USCIS shall establish a nonprofit entity to spur innovation in the expansion of citizenship preparation programs and to support assistance for immigrants seeking permanent resident status or citizenship. The bill also requires the Department of Homeland Security to (1) report to Congress before increasing fees for immigration adjudication and naturalization services above the levels of such fees on January 1, 2019, and (2) waive or reduce certain immigration-related fees for low-income aliens. The bill also (1) waives the English proficiency requirement for the naturalization of certain permanent residents, (2) repeals the public charge ground for deportation, (3) requires states to provide for automatic voter registration to qualifying new citizens unless that individual declines, and (4) sets a floor of 125,000 to the maximum number of refugees who may be admitted into the United States each year.