But despite the similarities, a conflict with Iran would not simply be a redux of the 2003 war with Iraq. It would be quite different in many ways - and it would almost certainly be substantially worse.
Present-day Iran is a significantly different country compared with Iraq in 2003. The way it would fight a war is very different, too.
If nothing else, Iran is simply a bigger country than Iraq was before the 2003 invasion. At the time, Iraq's population was about 25 million. Iran's population is estimated to be over 82 million. Iran spans 1,530,000 sqkm of land, compared with Iraq's 435,000 sqkm.
One estimate from 2005 suggested that the Iraqi Army had fewer than 450,000 personnel when the invasion began. Recent estimates suggest that Iran has 523,000 active military personnel, as well as 250,000 reserve personnel.
Just as important, however, is Iran's location. Unlike Iraq, Iran is a maritime power bordered by the Caspian Sea to the north and the Gulf and the Gulf of Oman to the south. It shares land borders with several troubled US allies, including Afghanistan, Pakistan, Turkey and Iraq.
Its location in the centre of Eurasia is particularly important for trade. About a third of the world's oil tanker traffic passes through the Strait of Hormuz, which is bordered by Iran and Oman. At its narrowest point, this shipping route is just under 3.2km wide. Blocking it could lead shipments of daily global oil exports to drop by an estimated 30 per cent.
In terms of conventional military strength, Iran is far weaker than the US. But the country has long pursued asymmetric strategies that could allow it to inflict serious damage on US interests in the region.
Iran's Revolutionary Guard Corps, a force loyal to Iran's supreme leader, Ayatollah Ali Khamenei, and separate from the regular military, has an external special operations arm known as the Quds Force that has helped build proxy forces in places such as Iraq, Lebanon and Syria. It funds militias such as Hizbollah, which is powerful in its own right.
Iran has used these type of groups to target Americans before. Earlier this year, a revised Pentagon estimate found that Iranian proxy forces had killed at least 608 US troops in Iraq between 2003 and 2011. Iranian proxies could cause havoc in Iraq and Afghanistan again.
Iran's navy has a real advantage against the United States, too. It doesn't need big ships or firepower to block off the Strait of Hormuz, for example, but could use mines or submarines to force a halt in trade.
US war games have suggested that speedboat suicide attacks and missiles could be surprisingly effective against the American military. A 2017 report from the Office of Naval Intelligence found that the navy of the Revolutionary Guard, which is distinct from Iran's regular navy and focuses on smaller and faster but still heavily armed vessels, had received more responsibilities to protect the Gulf.
Then there's Iran's ballistic missile programme, which the Missile Threat Project at the Centre for Strategic and International Studies describes as "the largest and most diverse missile arsenal in the Middle East." The threat from Iranian missile technology extends beyond the country's borders, too: Hizbollah is thought to have an arsenal of 130,000 rockets.
If the US were to engage in a military conflict with Iran, it would probably require significant manpower that would otherwise be used to check bigger powers such as China or Russia. The New York Times reported yesterday that Trump's acting Defence Secretary, Patrick Shanahan, drew up plans to deploy 120,000 US troops to the region if Iran attacks American forces or restarts its nuclear programme. This was based on a scenario that did not involve an invasion, which would require more troops.
The invasion of Iraq involved 150,000 US troops, along with tens of thousands from allied nations. The financial cost of the Iraq War was pegged at over US$2 trillion in 2013, with about 400,000 people estimated to have been killed between 2003 and 2011.
American military planners know all this. However, the US government cannot say that there are no good options to militarily engage Iran, because doing so would take the threat of military action off the table and diminish the pressure that it hopes to maintain on Tehran.
It's a risky strategy that has even some of America's closest allies worried.