It was an autographed card of Bill Hayes of the Yankees, featured with a picture of Joe DiMaggio. I hadn't heard of Hayes, but that's not uncommon for some of the lesser known players of the '30s.
I had some digging to do.
From what I can tell, Hayes never made it to the Majors. The back of the card says that he spent 14 years in pro ball, but I assume they were all in the Minors. I can't find any of his stats, however. Perhaps I am not very good at Google.
The most info I can find comes from his obituary (credit: Amarillo Globe News):
Bill spent 16 years in professional baseball, starting in the spring of 1937, including two years in spring training with the New York Yankees. During his baseball career, he also served the Chicago White Sox, Boston Braves and Detroit Tigers. After the 1951 season, he appeared on the cover of the Sporting News magazine as the Minor League Executive of the Year. In 1954, he moved to Texas and became well known as a pioneer in developing a two-party state. He won the first contested Republican primary for lieutenant governor of Texas and delivered more than 1,300 speeches. In 1964, he was nominated unopposed as U.S. congressman-at-large and was a delegate to the Republican National Convention pledged to Sen. Barry Goldwater in his bid for the presidency. He flew with Sen. Goldwater to many cities, including Amarillo, where he spoke preceding Sen. Goldwater's address.Interesting. It looks like he was obviously a very bright and well-rounded guy to play pro ball for so long, serve as a successful minor league executive, and then have a very accomplished career in politics.
As for Big League Cards in Teaneck, NJ, here is a Google image of the office since the address was listed on the card.
Check out the website here. It was most recently run out of Dayton, OH, although the link no longer works to order cards. But clearly the same card design!
So many questions still unanswered, but this is certainly one of the more unique cards I've ever received from another blogger.