NEWS FROM WASHINGTON.; Meeting of the Thirty-Seventh Congress. A Quorum Present in Both Houses and Business Proceeded with.The President's Message to beDelivered To-day. Some Hints of the Contents of the Department Reports. Six Hundred and Sixty Thousand National Troops in the Field.The Question of Admitting Representatives from Seceded States. Resolutions in Favor of the Confiscationof the Slaves of Rebels.THE FATE OF THE REBEL ENVOYS. The President is Recommended to Treat Them the Same as Cols. Corcoranand Wood are Treated. SPECIAL DISPATCH FROM WASHINGTON. THE ASSEMBLING OF CONGRESS. THE FEELING ON THE SLAVERY QUESTION. POPULAR MEASURES. NUMERICAL STRENGTH OF THE ARMY. COLLECTION OF SOUTHERN DEBTS. IMPROVEMENT OF THE ARMY AND OTHER QUESTIONS. THE POSTMASTER-GENERAL'S REPORT. A SERENADE AND SPEECHES. TREASURY NOTES TO BE REDEEMED. REBEL CAVALRY IN A CLOSE PLACE. THE REBELS DOWN THE POTOMAC. A CALL UPON THE PRESIDENT. PRISONERS IN RICHMOND. DID NOT MEET THE REBELS. ZOUAVE UNIFORMS FROM FRANCE. TO BE PROMOTED. PROMOTED. LONG BRIDGE

WASHINGTON, Monday, Dec. 2.

Congress assembled to-day, and contrary to expectations, more than a quorum was present in each House. From the Senate, BRECKINRIDGE, of Kentucky, and JOHNSON, of Missouri, were absent -- both now holding commands in the rebel army. Senators POWELL, BAYARD and POLK, whose sympathy with the rebellion during the extra session and since were too apparent to be consistent with their resuming their seats, were nevertheless present. JOHNSON, of Tennessee, was absent, being now near his home looking after the interests of his constituents.

In the house some seats were vacant which were occupied last session. BURNETT, of Kentucky, is now in active rebellion in his own State. BEN. WOOD is in New-York, probably engineering to forward the interorests of FERNANDO I. in to-morrow's election. Mr. ELY, of Rochester, is in the custody of the rebels. KERRIGAN, of New-York, is in the custody of the military authorities. HENRY MAY, of Baltimore, unexpectedly appeared, he having been released from his parole, order of the State Department, that he might resnme his seat, and the House take cognizance of his case. VALLANDIGHAM was also present, and, though meek in comparison with his attitude in past years, yet his sympathy with the rebellion showed itself several times during the proceedings. Several members who hold commands in the army were absent, among whom were PHELPS, of Missouri, and GEARY, of Pennsylvania. Others, similarly situated, were present, among whom were FRANK BLAIR, who moved the expulsion of REID, of Missouri, who is now in rebellion against the Government; VAN WYCK, of New-York, who is in his seat during the day and in his camp at night.

The House had hardly become organized before propositions were introduced relative to the policy to be pursued in reference to the slaves of rebel masters and the vote on the motion to lay one of them on the table showed a preponderance in the House in favor of some measure looking to the confiscation or emancipation of the slaves of rebels. As a proposal to postpone the discussion of the matter for a week was readily carried, there is evidently no desire for any hasty legislation upon the subject.

The deepest feeling, and almost excitement, prevails among the Union members of Congress from Western Virginia, Kentucky and Missouri in regard to the future policy of the Administration. The most prominent among them, and those who have labored most earnestly from the beginning against the Southern rebellion, declare that the inauguration of the Abolition policy of the war, and a movement looking to the arming of the slaves, will instantly throw the three States named into the Southern Confederacy, and annihilate the great National armies in Kentucky and Missouri, in fact, all National organization west of the Alleghany Mountains.

Several members of the House of Representatives belonging to the Democratic Party, on learning that the Message of the President is highly conservative, determined to call upon him in a body to-morrow, or next day, after the Message had been delivered, not only thanking him, but expressing their admiration of his firmnees in standing by the Union and the Constitution, and refusing to adopt the radical ideas of the Abolitionists in regard to arming the slaves.

TWELVE O'CLOCK AT NIGHT. -- I am enabled to state in the most positive manner that the struggle is over, and that the President's conservative policy is sustained by his Cabinet with entire unanimity. The Message will go in to-morrow in exact accordance with the foreshadowings of your correspondent. There was much less dissension in the Cabinet from the President's views than has been supposed to exist and now all difficulties are reconciled, and the Government is a unit.

The feeling of the House and the people on the subject of sustaining Commander WILKES was shown by the unanimity with which the vote of thanks to him was passed, and the words of satisfaction that passed along the galleries. When the resolution calling upon the President to confine MASON and SLIDELL in felons' cells so long as Cols. CORCORAN and WOOD were so treated by the rebels, the applause that resounded from the gallery showed how deep was the feeling of the people upon the subject of the barbarous treatment of those gallant men.

The figures I sent a week ago regarding the strength of the National army, will, I am confident, be fully confirmed by the forthcoming report of the Secretary of War. The effective force at the disposal of the Government now rises to the enormous aggregate of 660,000 men, (including regulars,) -- of whom, in round numbers, 550,000 are Infantry, 54,000 cavalry, and 20,000 artillerymen, besides sharpshooters, engineers, &c. Of this force New-York supplies over 100,000 men,the largest number furnished by any State of the Union, though Pennsylvania and Ohio follow very close behind. The five Slave States of Kentucky Missouri, Maryland, Delaware, and Western Virginia, furnish close on 60,000 men to the army of the Union. The great Powers of Europe will learn, from the figures of the Secretary of War, that, judged by their own standard, the Union also is a great Power; and that, if large armies are the test of the strength of a Government, there is yet a powerful cohesive force in the American Republic.