You can find the NY Times Article mentioned above on line by goggling “thorough, out-and out, unconditional Unionist” --be sure to use the quotes. Sterling Price ran for office and was elected as an "Unconditional Unionist" but he "jumped ship and became a rebel. The U U party was active in the slave states that remained in the Union, especially Missouri, Kentucky, West Virginia and Maryland. For a breakdown of the 38th Congress see
http://en.wikipedia.org/wiki/38th_United_States_Congress. Members were normally elected rather than appointed. People within the Confederacy who were pro-Union would have had much the same opinion but have no opportunity to vote unless under occupation.