Try studying your history more closely. Gen. Scott and his forces landed at Vera Cruz, defeated a much larger Mexican army marched overland to Mexico City, defeating forces on the way that combined could have overwhelmed him at more than 10 to one odds, then after the Battle of Chapultepec, marched into Mexico City with an American flag flying over their government buildings. The Mexican forces under Santa Anna were driven away.
Gen Scott was offered the military dictatorship of Mexico by the remaining Mexican government after their surrender. He was offered the "whole enchilada." He turned them down cold because he was an honorable man and also knew that was not the kind of victory a nation like America would pursue.
We not only kicked their ass, but paid them as well.
After annexing Texas, the US began negotiations for the purchase of the western territories that became New Mexico, Arizona, and California. The price tag was a little over 30 million. Part of the deal was to get an agreement on the Texas border. The treaty that established the Republic of Texas at the Rio Grande, the Mexican government was insisting it was now Neuces. The Mexican government changed after a revolution, the Slidell deal was off, new Mexican nationalism led to the new government declaring a defensive war against the US.
Not long after, Mexican troops crossed the Rio Grande, killed Texan settlers, and engaged US troops in the area. Polk then asked Congress for a declaration of war.
After the US forces defeated the Mexican army in Mexico City, Santa Anna was on the run and fled the country. The new Mexican president began negotiating with Trist, who had been recalled by Polk but remained anyway to continue negotiations. The first treaty efforts were derailed by Polk's reaction to Trist's disobedience and the MExican government's stubbornness and pride. Trist's further negotiations resulted in the final treaty.
Lower California and Arizona were not part of the peace treaty. That treaty formally recognized the borders of Texas, and gave the areas of New Mexico, part of Colorado, and upper California to the US. The original demands for the ceded territories was over thirty million. Negotiations stuck at 15 million. At this point, Polk acceded to public pressure in an election year with an electorate tired of war and casualties. He submitted the treaty to Congress as it met his demands for the new border and he begrudgingly recognized that the new Mexican government needed funds to rebuild and that further war would have torn the US apart. Fifteen million was a small price to pay to rebuild two countries.
It wasn't the best treaty and Polk knew it. He also knew that the cause of the war had been settled with the treaty defined borders, the attacks on America had been repaid and further attacks were not going to come, and a lasting good peace was possible. Overall, as Truman once said, "Polk was a great President. He said what he was going to do and did it." Polk said he would settle the issue of war with Mexico for good, and he did it. No Americans suffered from war with Mexico since.
Presidents Polk and Bush share the same pitiful lack of gravitus. Americans then and now are paying dearly for that immense character flaw.
Pres. G.H.W. Bush on the other hand, was handicapped by different circumstances. No Arab nation was going to open their borders to US only forces and we couldn't mount a successful large-scale amphibious invasion without ground support. So an alliance had to be formed to satisfy all demands whether European or Arab, and the iron promise of repelling the Iraqi invasion of Kuwait and not removing Saddam had to be given - otherwise, not only would we have no bases in Saudi Arabia but we would be facing wider war with the other Arab nations.
Even though it was the right thing to do to go after Saddam then and even though Bush knew it was a terrible mistake to leave him alone, it was the only way to free Kuwait. To go after Saddam anyway would have broken our word, dishonorable and fatal to any further progress in the Arab world.
Keeping that word, even though it led to further problems, gave the US opportunities and even some support after 9/11. Deliberately making the mistake then set the stage to make the invasion of Iraq a possibility now.
G. H. W. Bush made mistakes in his presidency, most of them domestic and trusting the Democrats, but stopping short after Kuwait was one he promised to make. Keeping your word is a large part of gravitas - even if that word is a Left buzzword.
See: http://web.nmsu.edu/~publhist/colhist.htm
"Columbus, New Mexico, in the early spring of 1916 was a sleepy little border town. As the Mexican Revolution raged to the south, most Americans perceived little threat from this conflict, including many of Columbus' citizens, who felt safe in their village. To add to this feeling of security, a detachment of approximately 350 U.S. Army soldiers from the 13th Calvary stationed at Camp Furlong on the outskirts of Columbus stood between Mexico and the town.
In the middle of the night on March 9, 1916, life in Columbus changed dramatically. At 1:00 A.M., between 500 and 600 Mexican revolutionaries, led by General Francisco "Pancho" Villa, crossed the border into the United States. Villa divided his troops and attacked Columbus from the southwest at approximately 4:20 am. This attack caught the entire town, as well as the army camp, by surprise.
The Villistas concerned themselves more with raiding than killing, otherwise the town might have been erased. That morning majority of the destruction of the town came from the burning and pillaging of the business district. Surprisingly, the army camp and stables received little damage, even though the horses and armaments must have been attractive to the raiders. Alerted by the gunfire and burning buildings, many Columbus residents fled to the desert, or sought refuge in the school house, the Hoover Hotel, or private homes. The noise and fire sealed the fate of the raiding Mexican Army. U.S. Army officers and soldiers, awakened by the commotion, set up a Benet-Mercier machine gun in front of the Hoover Hotel and produced a murderous rain of bullets. Another machine gun set up on East Boundary Street fired north and caught anyone in the intersection of Broadway and East Boundary in a deadly crossfire. The raid lasted until dawn, or approximately one and a half hours. By this time, the death toll totaled 70 to 75 Villistas. In addition, during the attack on Columbus, eighteen Americans, mostly civilians, died."