Hi Megan -- thanks for posting to History Hub!
You can start by searching Chronicling America, a Library of Congress website that provides access to information about historic newspapers and select digitized newspaper pages from 1777 to 1963.
I'd also recommend checking with local public or academic libraries to see if they offer access to any historic newspaper subscription databases -- there are several.
Representative Andrew May served as Chairman of the House Committee on Military Affairs in 1943 (the 78th Congress). However records of a press conference held by an individual Member of Congress wouldn't be part of the committee papers that make up our holdings.