McCloskey presented credentials as a Democratic Member-elect to the Seventy-first Congress and served from March 4, 1929, to February 10, 1930, when he was succeeded by Harry M. Wurzbach who successfully contested his election. Wurzbach had made allegations of gross fraud in Bexar County and when the House committee investigating that claim demanded to see the election records and to recount sundry ballots, McCloskey instead appeared before the committee and conceded stating that "I am satisfied that I was not elected and that Mr. Wurzbach was elected, and I am contending no further in this matter."[1] Vote totals were revised and instead of winning by 319 votes, he was found to have lost by 61 votes.
He was not a candidate for renomination in 1930. He resumed the practice of law. He served as judge of the corporation court of San Antonio, from January 1943 to July 1947. He practiced law until his death in San Antonio on July 21, 1950. He was interred in San Fernando Cemetery.
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