What do you mean exactly? In purely technical terms there hasn't been a "technology needed" to cross the Atlantic since the Bronze Age--Heyerdal, crazy though he was, showed with Ra II that it was at least practically possible for Egyptian reed boats to cross the Atlantic, however absurd and dangerous an actual expedition might be. The Romans, who traded with India by ship, were surely more capable of reaching the New World than the reed boats that Heyerdal got across in. But does that mean that it was likely? No. Far from it. What it does mean is that, technocratic though we may think history is (thanks EU IV), pure capability does not translate to actual action--there were plenty of reasons why the Atlantic wad not crossed, and technical inability was not one of them, though such a voyage would've been extremely dangerous (hell, it was dangerous even when Columbus did it more than a thousand years later)

Pinning on a second question: Even if they did, would Rome have had the motivation to go exploring at all?