I'd have to say that there'd be a lot of oppositon to the idea, both in terms of cost, and going against the weight of professional naval opinion based on what was known at the time, even if US industry at the time was capable of building large iron warships.
At this time, the RN was also experimenting with unarmored iron hulled warships, and it was found in a series of trials against mockups of iron hulls & a target ship between 1845-50, that high-velocity shot impacts would make a clean hole, but low-velocity ones would make jagged ones with lots of splinters that'd be difficult to plug (much more serious issue than on a wooden ship), & thick plates could also produce dangerous clouds of shrapnel, before finally concluding that iron as is was unsuitable for warship construction. Although this contradicted earlier combat results from HMS Nemesis in China during the Opium War & the Mexican frigate Guadelupe against Texan forces in 1843, analysis of samples taken from HMS Warrior during her 1980s restoration found that the ability of iron to resist sudden impacts, such as incoming fire was highly dependent on temperature, becoming brittle & likely to shatter in cold weather such as when those trials were conducted or that might be found in the North Atlantic- the earlier engagements were in warm waters- making the 1850 findings reasonably correct at the time. Battleworthy iron warships had to wait a few years for the development of suitable armor & metallurgical advances, combined with the use of wood backing to help with shock & splinters.
Furthermore, unless the gun explosion on the Princeton (first USN screw-propelled ship, but made of wood) is butterflied away somehow, the fallout from that disaster could have the effect of discrediting new innovations (IOTL, the designer of the Princeton, John Ericsson, who arranged for a lot of innovations in the ship's design, but wasn't responsible for the defective gun, was scapegoated for political purposes, & this could be extended to other radical new innovations
I'd think that a better POD to achieve an earlier all-iron/steel USN would be around 1865, where for whatever reason, the US decides to build & maintain a modern navy instead of relying on already-obsolete ACW leftovers (mostly wooden steam frigates, sloops, & corvettes) for another 20 years.