Never thought about this before, it's intriguing as are the arguments.
1. Britain is a worldwide empire in 1848 which also means it's Navy and Army are needed all over the world pretty much where they are to hold down the grumpy natives all scattered months of sea travel apart from each other and the British Navy like any doesn't have an endless number of troop transport and cargo ships to move them around easily. England's comparatively small population, i.e. compared to India, South Africa, Sudan, Egypt, Malaysia, Hong Kong & China sites, it's Pacific Islands, British Guiana, it's Carribbean Islands-Jamaica, Bermuda, etc. is stretched very thinly. Massing ships or troops, let alone transport or building a massive new army, would be a much smaller available/transferrable number than seem to be posited here. 1848 is also the year of major rebellions all over Europe and Latin America, which makes keeping more troops close to home quite appealing.
2. I don't know what the U.S. Navy looks like in 1848. Smart commanders we see in the Civil War like Farragut and Porter would be mid-level officers or even ships' captains by this point and the American shipbuilding industry was in full swing in part from the demands of the American whaling fleet (who oddly would probably be a major resource coming from their Pacific hunts to Oregon, probably as privateers) so a longer war would allow building new American frigates with a large merchant marine to draw on along that same coast that's too long for the British Navy to fully blockade (assuming the British Navy isn't pulled from all over the world in entirety and left on the American coast.) Once again the Americans would issue privateer licenses to it's merchant ships, still an era of cutting some gunports in and making simple muzzle-loading cannons as we were able to in previous wars with far less of a metals industry than 1848. That'd draw off a lot of the British Navy away from coastline blockades.
3. Finance. Loss of the American cotton crop to British textile mills would be devastating and if this led to the British turning Egypt into a private cotton plantation 12 years sooner, that'd greatly decrease the economic power of the South when it rattled it's sabers about seceding. For both sides, the surprise costs of any level of open warfare would push hard towards a speedy peace, but hideously costly wars over very small issues are more common than reason would suggest.
4. American army: Winfield Scott, one of our ablest Generals ever, is in charge and had done well against British troops in the War of 1812. Many of the best commanders in the American Civil War are in the Army or recently at this point and freshly tested by the Mexican War along with years of Indian fighting (we were pretty much continually at war in many places across the continent...asymmetric guerrilla warfare that would be oddly useful training if applied to the British land forces. In 1848 the Sharps breechloading rifle has just been patented and derives substantially from John Hall's breechloading 1819- Army flintlock rifle in common use in the Mexican War, mfd. deep in Virginia at Harper's Ferry. Colt's revolvers and revolving rifles are back in production and in Army issue by this point which makes cavalry considerably more devastating with sets of revolvers as the Texas Rangers had just been figuring out...bad news for British lancers, dragoons, light cavalry, and artillerymen. A horse or mule-carried artillery piece, the mountain howitzer, is Army frontier issue by this point I think and would also be a nasty surprise. American soldiers to an even greater extent than the Civil War would be more like Confederate troops in mostly coming from farms with better health, more rugged constitutions, far greater familiarity with the outdoors as well as hunting, and more independent than the city and village dwellers English press gangs had found.
5. America has vast numbers of horses, wagons, riverboats/barges/canal boats, steamboats, a few railroad lines and locomotive works, and considerable industry by this point. The comment about all American cities being accessible to the Royal Navy's assaults leaves out Pittsburgh, Cincinnatti, Nashville, Memphis, St. Louis, Atlanta, and smaller inland towns and cities with millions of residents, major resources, and growing industry that would remain inaccessible to the British but logistically connected by rivers, canals, roads, and increasingly railroads (a surge in rail construction and upgrading bridges and major roads seems inevitable with interesting consequences too.) America already had more population than England by the time of the Revolutionary War (and has along with explosive natural population growth due to better nutrition and cleaner water, had considerable waves of Irish (potato famine 1840's, big surge 1790's) and German immigrants (to the point that inland often the language is German)...many of them veterans of European armies and not warmly stirred by the sight of the British flag.
6. It would have to be after the Mexican War to work as others have pointed out. Without that, the U.S. has no Pacific ports (no San Francisco, San Diego, etc.) to support an Oregon campaign logistically. The Gold Rush either hasn't started or is just commencing, Sutter's Mill's discovery is 1848, which drew several hundred thousand Americans there in the next couple of years...which would make a campaign for the rest of the Pacific Northwest vastly easier to do. Otherwise there's a few missionaries and early settlers in the Oregon Willamette Valley (far less than the Canadian community at Fort Vancouver then I think), even fewer fur trappers (too late), and the major waystations for resupply are fur trading posts serviced by Missouri steamboats/riverboats (Ft. Benton, Montana) or Fort John/Fort Laramie in South Central Wyoming's prairies, Bent's Fort, etc. a vast distance to Oregon.) The British with the Hudson's Bay Company fur trading empire across Canada would be vastly better positioned to enlist natives like the Blackfeet Indians again to retain and defend the region at very little cost. Moving American troops or more likely volunteer irregular units from St. Louis etc. might have them stumble across the placer gold fields in Colorado, Montana, Idaho, and Oregon 10-20 years early (which could turn military expeditions of such into sudden gold camps abandoning their mission or at least delaying it by months or years.)
I suspect the British wouldn't readily give up the Pacific ports of Canada, that's a huge deal for a maritime power in the age when everything that could moved over water instead of land and the sun never set on the British Empire. Interesting idea.