I think the idea is Britain agreeing a Mexican offer to buy California at a point where Mexico knows that there is now nothing else they can do to stop the USA attacking them to take it over. A bit of a "if we can't have it, you can't have it either" philosophy, if you will.
That would assume that Mexico knew, expected, or thought they would lose the war. They didn't, and had little reason to. The Mexican Army was much, much bigger, and pre-war newspapers and editorial-generals expected to go through Mexico, fighting around New Orleans, and possible marches through the South to liberate slaves and put a bloody nose to the one part of the US interested in the war.
Because, and most everyone knew this, Mexico had by far the bigger army. Mexico thought itself a natural great power as well, future leader of the South (America).
Of course it was a conscript army, it wasn't well organized or equipped, they didn't have the logistical base to do any such thing...
But no one realized that before the war, or fully understood it. This is a case of 20-20 hindsight, in which the American success was just so obvious, and anything else is simply silly. Mind you, this also forgets how near-disaster the US could have come to. Being run back into the seas outside of the Mexican capital, for example, would have changed a lot.
Dean
I could see it being unpopular with the US, whether before or after an agreement on Oregon and that it doesn't really make that much sense after an agreement. However why would accepting an offer from Mexico upset any of the Latin American states? Might see some resentment in Mexico if a later government objects to its predecessor making the sale but that's about it.
Because there wouldn't be an offer from Mexico, for the same reasons the natives of Latin America weren't fawning over themselves to sell themselves into the US for pennies an acre. Santa Anna considered, not even necessarily strongly, selling California to the US not for it's own sake or for profit, but as part of a greater settlement to a boundary dispute over the Texas border, which was far more important to Mexico. Whether Santa Anna could ever have even gotten such an agreement past the Mexican Congress is indeed in doubt (the propped up government that ended the war fell almost immediately after signing the American surrender documents), and there is little, if any, similar reason to sign the territory over to the British. Mexico did not need or want the gold (the American payments were in large part a salve on American consciousness), however loosly it held California it did hold it, and Britain doesn't really have anything else to offer. After the Oregon settlement, Britain doesn't even have a border.
A British California doesn't come from sale, short of changes that make Mexico not Mexico. It comes from partitioning Mexico, and almost certainly not with American agreement. Such an act
will spoil much of Britain's good relations with Central/South/North America, which were built upon a reputation of not conquering and colonizing the New World.