Full searches for the US should not only include searches of the Federal Register (including International Registrations covering the US) but also the individual State Registers and a Common Law search for any unregistered rights.
I think we would all agree that not undertaking any checks would be a bad idea. Beside the USPTO's TESS database, which is great for identical searches, I would refer you again to the Markify database which can provide a more intelligent search and catch many killers. Remember it does not claim it will find every similar mark, but then who can do that anyway?
Many of the State Registers are on-line and searchable but there's 50 of them and it would take you a while to conduct identical searches across them separately. Commercial databases are often better for this and with one tick of "US State" you can search all 50 of them in one go, including the ones that are not available to search through their Secretary of State's website. Some check Puerto Rico too meaning it's actually 51 databases being searched. You will probably have to pay on a per-hit basis unless you have a subscription and this covers the US State database.
You could omit the individual States because most - although I don't believe it is all - States operate a registration system that confirms any common law rights in existence i.e. use is a prerequisite for registration. This leads us nicely on to Common Law searches.
The cheapest Common Law search out there is an internet search. Whether you restrict to the most popular search engine, Google, or extend it to others like Yahoo and Bing would be up to you. There are obvious limitations to this approach and it is absolutely far from a catch all. It is generally restricted to identical matches although Google sometimes makes alternative spelling suggestions. You could also rely on market intelligence you/your client may have or can leverage e.g. through a local distributor who may know about similar marks already on the market.
For foreigners filing in the US particularly via the Madrid Protocol, where time is on our side and penetration of the US market is not expected imminently, we could take a relaxed view and just file from here. It would be a "suck it and see" approach to see what issues are raised, if any, by the USPTO. It would be important to file for an acceptable specification, which you may or may not be skilled at drafting, and not a "Europeanised" broad specification, but this is another discussion. It's also important to realise that any Common Law rights will not be revealed by an Examining Attorney.
In an ideal world, a full search (Federal, State and Common Law) with legal opinion would still be requested through a US trade mark lawyer. They would be able to advise on negotiating around possible problems, for example, by carefully crafting a specification of goods or providing an opinion on a 50/50 mark where you really need a detailed knowledge of local practice and case law. There is a lot of value a US trade mark lawyer could add to a matter. However, you may be able to knock out trade mark candidates far more cheaply before you go to them for a final (hopefully) green light to file or use. Adopting this approach could mean you knock out candidates that could possibly be available, but you may evaluate that risk as acceptable.
Overall, don't underestimate the number of free tools available to you. This is not an ideal economic environment and you have budgetary constraints. You have to weigh up costs versus risk. When it comes to the crunch, rely on a US lawyer to be absolutely sure.