Another name for it is the camel’s nose under the tent: get some sort of minimal involvement in another country and once you’re in, expand the mission. From Ted Galen Carpenter at theamericanconservative.com:
Unscrupulous used car dealers could learn a trick or two from America’s foreign policy mandarins when it comes to bait-and-switch tactics. Repeatedly, U.S. officials have invoked a specific justification—frequently an emotionally charged one with wide appeal—to obtain congressional and public support for a military intervention or other questionable policy initiative. When the original justification subsequently proves to be bogus, exaggerated, or no longer applicable, they simply create a new rationale to justify continuing the mission.
That tactic is especially evident with respect to the seemingly endless war in Afghanistan. U.S. leaders justified the initial invasion of the country as a necessary response to the 9/11 terrorist attacks on the United States. Foreign fighters belonging to Al Qaeda had used the country as their primary safe haven, and the Taliban government had allowed Osama bin Laden and his organization to plan and execute the attacks from that sanctuary. Given the public’s emotional trauma from the 9/11 episode, the nearly total lack of opposition to launching the Afghanistan invasion was unsurprising. In statement after statement during the initial months and years that followed, American officials reiterated that defeating Al Qaeda—and, if possible, killing or capturing bin Laden—was the primary objective. Ousting the Taliban regime was a corollary to that goal, but no one advocated a long-term war against that indigenous Afghan faction, however odious its social policies might be.