The military is conducting multiple reviews of security procedures in response to the shooting, including looking at the security clearance process.
Before the Navy Yard hearing, Congress will try to avert a government shutdown, which will occur on Tuesday if no measure is passed to fund the government.
The Senate on Friday passed a stopgap funding measure after restoring funding to ObamaCare, sending the measure back to the House and setting up an eleventh-hour showdown.
On Saturday, the House passed a measure to delay ObamaCare for one year, as well as a bill that would fund the military in the event of a shutdown, which could spare the Pentagon if the government shuts down.
The Pentagon and other federal agencies have been preparing for a shutdown over the past week, repeating many of the same steps the department took in 2011 when a shutdown was narrowly averted.
Service members will continue to work in the event of a government shutdown, although they will not be paid until it is resolved.
Civilian Pentagon employees who are not on an exempted list of more than 40 activities will be furloughed. In 2011, roughly half of Defense Department civilians were faced with furloughs in the event of a shutdown.
Defense Secretary Chuck Hagel will be far away from the Capitol Hill budget battles, traveling this week to South Korea and Japan.
Secretary of State John Kerry will join Hagel in Japan for talks on the U.S.-Japan security agreement.
Before heading to Japan, Hagel will stop in South Korea to commemorate the 60th anniversary of the U.S.-South Korea defense treaty. He will also be on hand for the change of command ceremony for the head of U.S. Forces Korea.
On Capitol Hill, hearings are expected to go on as scheduled, shutdown or not.
The House Armed Services Readiness subcommittee is holding a hearing on Thursday looking at the readiness impacts of sequestration.
On Thursday, the Senate Homeland Security will hold a hearing on “threats to the homeland,” where acting Homeland Security Secretary Rand Beers, Director of the National Counterterrorism Center Matthew Olsen and Deputy FBI Director Sean Joyce will testify.
The House Foreign Affairs panel is holding a hearing Thursday to discuss the threat posed by al Qaeda affiliate al-Shabaab, which took responsibility for the Nairobi mall attack earlier this month.