ORGANIZATION OF THE UNITED STATES HOUSE OF REPRESENTATIVES. – This body is now, without doubt, engaged in an animated struggle for the election of its officers. It seems to be supposed that recent events have forced a union between the regular Democrats and Southern Opposition members. This combination, if complete, would command 115 votes, and would leave 122 members classed as Republicans, anti-Lecompton Democrats and Independents. The information before us induces us to believe that the coalition most likely to prevail is one between the Republican, anti-Lecomptonites and irregulars. All the members included within these three classes were elected in opposition to regular Democratic candidates, by Republican votes. The first of these circumstances furnishes a reason against concurrence by them with any proceeding designed to advance the interests of the Democrats as a party, and the last is a bond of union with the Republicans not likely to be broken through by those members looking to a reelection. The total number of members elected upon the Republican sentiment, and as representatives of it, is 121, a clean majority of 5.