The Wikipedia article about the report itself has a lot of information (which Denis has since posted).
There are 4 levels, Tier 1, Tier 2, Tier 2 Watchlist, and Tier 3. Romania which has been Tier 2 as long as the report has existed, has fallen from Tier 2 to Tier 2 Watchlist.
"Countries whose governments do not fully comply with the TVPA’s minimum standards, but are making significant efforts to bring themselves into compliance with those standards"
As far as the actual question, there's very little that will actually happen from this because Romania hasn't been downgraded a full tier. However, US policy states that countries that do not sufficiently meet the US standards to combat human trafficking won't receive "nonhumanitarian, nontrade-related foreign assistance."
Further, Romania is only projected to receive 1.5 million from the US in 2019 (total), at least some of which seems to be humanitarian aid. While any that isn't might have some impact, in the scheme of things, the US isn't significantly investing in Romania anyway, so even if they lost all of the 1.5 million (they wouldn't), it would be a small drop in the bucket for Romania's total GDP.
As far as non-official forms of recourse, they are much more subjective, so I don't really want to go into them in this answer as it would be entirely opinion, but it is worth noting that they might exist, but would be relatively minor.
Ok, lastly, promise...it's also worth noting that Romania spends 1.8% of its GDP on defense, falling just short of the 2% mandate by NATO. Only 5 countries reach the 2% threshold, and Donald Trump takes that number pretty seriously and has frequently criticized countries for not doing their part. At least under the current administration, I would say that taking this as anything other than a stern warning that this is an important priority to the US is reading more into it than merits.