The Constitution gives the President the ability to convene one or both Houses of Congress on extraordinary occasions. This should count.
Section. 3.The full faith and credit of the country is at stake. I urge the President to recall all of Congress, have the doors sealed, and force them to remain there until this is resolved.
He shall from time to time give to the Congress Information of the State of the Union, and recommend to their Consideration such Measures as he shall judge necessary and expedient; he may, on extraordinary Occasions, convene both Houses, or either of them, and in Case of Disagreement between them, with Respect to the Time of Adjournment, he may adjourn them to such Time as he shall think proper; he shall receive Ambassadors and other public Ministers; he shall take Care that the Laws be faithfully executed, and shall Commission all the Officers of the United States.
The government shutdown should not be a time that congressmen are allowed to go hobnobbing donor and fundraising - bring in the cots, and let's see how long they're willing to defend their actions.