A similar tactic was attempted in the days before a shutdown nearly occurred in 2011, but it did not come close to getting signed into law.
Part of the problem is that military pay is one of the most obvious signs that a shutdown is having a harmful impact.
Harrison and congressional aides said that military pay also is unlikely to be disrupted in the event of a short government shutdown.
Members of the military will receive their checks on Oct. 1, they said, and would still be able to receive the next scheduled paycheck on Oct. 15 if a shutdown only lasts a few days.
Cruz, who held the Senate floor for nearly 22 hours to protest ObamaCare, suggested last week that the House could pass a military-only funding bill as a response to the Senate.
GOP House leaders on Wednesday were mulling several different actions to take after the Senate passes a clean CR and sends it to the lower chamber, as expected.
DOD mulls cutting contractors from clearance process: The Defense Department is weighing whether to stop using private contractors for background checks in the aftermath of the Navy Yard shootings.
"I think that is something we need to look at," Deputy Defense Secretary Ash Carter said Wednesday.
Former Navy Petty Officer 3rd Class Aaron Alexis shot and killed 12 people during a shooting spree at the Navy headquarters in Southeast Washington, D.C., on Sept. 16 before being killed by law enforcement.
Alexis, who was honorably discharged from the Navy, gained access to the facility due to his status as a civilian contractor.
"Bottom line, we need to know how ... warning flags were missed, ignored or not addressed in a timely manner," Carter told reporters at the Pentagon.
Earlier this month, a Defense Department official told reporters that Alexis was not subjected to a reinvestigation for his security clearance after being hired for the IT job at the Navy Yard.
Reinvestigations for security clearances could be triggered when a former military member is transitioning into contractor or civilian service, according to Pentagon officials. But that only occurs if the time between retirement and re-entry is more than two years and if “derogatory information” is uncovered, officials say.
Concerns over how Alexis and other civilian workers receive security clearances reached a fever pitch on Capitol Hill in the aftermath of the Navy Yard massacre.
"It may be time for a [congressional] review to see how well these contractors are doing their jobs" in terms of vetting candidates for sensitive national security positions, Sen. Jeff Sessions (R-Ala.) told reporters a day after the shootings.
Sen. Dianne Feinstein (D-Calif.), head of the Senate Intelligence Committee, said last Wednesday the panel planned to hold hearings on the security clearance process.
Syrian rebels kill top al Qaeda leader: A top commander with al Qaeda's Iraq faction was killed on Wednesday as clashes between Syrian rebels and Islamic extremists in the country continued to erupt along the Iraqi-Syrian border.
Abu Abdullah al-Libi was killed when al Qaeda fighters engaged with anti-government forces in the northwestern Syrian border town of Idlib, according to al Alarabyia.
Officials from the Free Syrian Army, the largest and most organized rebel faction fighting in Syria, denied responsibility for al-Libi's death.
Sporadic firefights have begun to erupt along Syria's border with Iraq and Turkey, as rebel forces in the country are beginning to purge Islamic militant elements from their ranks.
Gunmen from the al Qaeda-linked group Jabhat al-Nusra exchanged fire last week with Kurdish fighters from the Democratic Union Party, a militant separatist group based in Turkey, according to reports.
Members from al Qaeda in Iraq and Jabhat al-Nusra, an extremist group tied to the terrorist organization, have taken a leading role in the rebels' fight to oust embattled Syrian President Bashar Assad.
However, rebel forces have begun to battle back against the terror group's influence among rebel forces, accusing the groups of co-opting the fight to overthrow Assad into an effort to expand al Qaeda's reach into Syria.
House Armed Services holding classified readiness briefing: Two Pentagon officials will provide a classified briefing on military readiness to the House Armed Services Committee on Thursday, according to a committee aide.
The committee will receive testimony in the closed briefing from Laura Junor, deputy assistant secretary of Defense for Readiness, and Brig. Gen. Martin Schweitzer, deputy director of regional operations from the Joint Staff.
Last week, the four military service chiefs testified before the panel on the impact of sequestration, warning that it was destroying military readiness.
The service chiefs have also been scheduled to testify next week before the Senate Armed Services Committee.
In Case You Missed It:
— Kerry signs UN Arms Treaty
— Senators unveil NSA reform bill
— Scalia predicts court will decide NSA spying
— FBI releases video of Navy Yard gunman
— Holder: No confirmation Americans part of Kenya attack
Follow us on Twitter: @DEFCONHill, @JHerbTheHill, @CMunozTheHill
You can sign up to receive this overnight update via email on The Hill’s homepage.