Probaby not a vector for an American monarchy, but one that would make monarchies more prevalent: the Mexican Empire survives. Agustin de Iturbide remains Emperor of Mexico in 1821. The Empire loses Texas to guerrilla warfare. James K. Polk never tries to become President, but he throws his influence over to Lewis Cass and helps him get elected in 1844. In 1845, Cass implements the same policies Polk would in OTL, starting the Mexican-American War. The only problem is that with the monarchy, Mexico has a stronger armed forces and is better united. The War goes on through 1848. Cass wins reelection by a small majority. Finally, Whig voices against the war, specifically Henry Clay who begins training his own political heir (just as Jackson did with Polk in OTL) in Abraham Lincoln. Lincoln gives thundering speeches through the House along with Robert Toombs. Finally, The war takes a turnaround when a Mexican offensive led by Santa Anna goes through Texas and even penetrates Louisiana and Missouri. (The goals were New Orleans and St. Louis, respectively). The attack fails, but it ruins all confidence in President Cass and the war effort.
In 1852, the Lincoln/Toombs ticket wins in a landslide. Effects:
1. Mexican War ends with a Mexican victory. Often termed the "Mexican Mistake." The border of Texas is redrawn, significantly reduced in size.
2. The Whig party remains a major American political party. The Democrats are eventually reduced to nothing when the Populists finally take over.
3. Mexico, formerly considered a weak monarchy, is now considered more powerful than the United States; nullifying the Monroe Doctrine, and proving that Monarchies are more powerful than republics.
4. California once sought help from the United States. Americans continued to feed arms and supplies to the Bear Flag Republic for a short while, but President Lincoln stopped that. Instead, the Californians look to Great Britain who is only too happy to oblige. California will eventually receive independence with a King on the throne in San Francisco.