THE WAR BEGUN. – The President and his party in the Senate have opened the campaign early against DOUGLAS. It was determined in caucus of the Senate last night that he must be ejected from his position as Chairman of the Committee on Territories. The object of this is merely to brand him as an unsound Democrat, - to notify the party at large that he is no longer to be regarded as in good and regular standing. It is one of those sagacious acts – those master strokes of party policy – by which Mr. BUCHANAN’S Administration is making itself famous and memorable. It is not supposed, in the best-informed circles, that Mr. DOUGLAS will commit suicide on hearing of this movement in the Senate.