Well, a naval program is no small thing to establish. And the American navy that came out of the program was a small, but very good navy with technologically superior ships. But it was expensive. The first Sec Nav benjamin Stoddert, in the 1799 program, even devised a plan to build 12 ships of the line (74 gunners) and several more frigates, which would have been a very impressive start for the USN. No doubt that would have raised eyebrows in Whitehall.
But I do not honestly know if the fledgling USA could pay for that, or even upkeep them.
USS Constitution (44 gun frigate) cost about $302,000 to build if my facts are close to straight, and everyone understands that building cost is far from all there was to upkeep and maintenance of a warship.
But Jefferson seemed to be inclined towards gunboats, and so the naval program did suffer from that. Gunboats are cheaper, but usually mounted only one or two heavy guns, and would be no match for a regular warship.
But, money was a problem in those days. With a population of about 5.8 millions souls, and a revenue (in 1803) of about 11.4 million dollars and a public debt of around 80 millions, a large scale building program such as Stoddert had in mind was pretty much beyond the realm of possibility.
Government Revenue Details: Federal State Local for 1803 - Charts
By comparison, Im sure the UKs expenditure on the Royal Navy would have dwarfed our entire Federal budget in those years.
So, its not like Jefferson had unlimited funds to work with. So, we must consider these things when we examine Thomas Jefferson through the lens of history.