We have intelligence from Mexico to the 5th of June. Political affairs seem to be in a confused and unpromising condition. Previous to the adjournment of the present Congress the Cabinet addressed a note to the Chamber of Deputies, asking them to take some decided step whereby to rescue the government from the difficult position in which it will be placed, without power or resources, and to save the nation from the necessary consequences of such a crisis. It was suggested that the government might be authorized to take, in connection with committees to be appointed by the Chamber, the resolutions necessary--such resolutions to be executed under the responsibility of the Ministry. This note was referred to a committee, which almost immediately reported that there was no reason why this demand for extraordinary powers should be granted. This report was adopted by a vote of 74 to 13. Congress adjourned on the 21st of May. The President's Address referred to the critical circumstances in which the country was placed when the Congress first met, which made it to be feared that its mission would be only the saddest duty reserved to man on earth, that of assisting at the burial of his country. The flame of war still blazed upon their frontier: negotiations designed to facilitate means of communication which would make Mexico the centre of the commercial world, had terminated in a manner to render possible a renewal of that war; and the commercial crisis had reached a development which threatened the domestic peace and the foreign alliances of the country. There was a daily increase in the deficit; distrust prevailed between the different departments; the country was fatigued by its convulsions and disorders, and weakened by its dissensions; and it seemed impossible to prolong the existence of the government. How the country had been rescued from such perils it was not easy to say, unless it were by the special aid and protection of Providence. Guided by its convictions and sustained by its hope, the government had employed all the means at its disposal, and would still endeavor to draw all possible benefit from its resources, stopping only when those resources should arrest its action. Fearing that this event might speedily happen, a simplification of the powers of the Legislature, during its vacation, had been proposed, instead of leaving all to the exercise of a discretionary power by the Executive. To this, however, the Legislature had not assented: and, consequently, the government considering its responsibility protected for the future, would spare no means or sacrifices to fulfill its difficult and delicate mission. To this address the Vice President of the Chamber replied, sketching the labors of the session, and saying that the legislative donation of the extraordinary powers demanded, could not have been granted without a violation of the Constitution--a fact with which the Executive should be deeply impressed.