I know that the official government position was pro-British and the Irish Republican Army was designated as a terror group, I suspect that was informed by the importance of the "special relationship" (especially the close personal relationship between Margaret Thatcher and Ronald Reagan) and the IRA's connections to the PLO, the ANC, Libya and the Soviets.
At the same time, the United States has a huge and influential Irish diaspora and it is alleged that prominent Irish American politicians on both sides of the partisan divide like Tip O'Neil (Democrat) and Peter King (Republican) more or less openly supported the IRA and much of the funding on the republican side came via organisations like NORAID in the United States.
Is there any polling data on the topic from the era?
A couple of quibbles with the question:
I know that ... the Irish Republican Army was designated as a terror group
Was it? I'm sure the US government was pro-British, but I'm not aware of any such designation for the Provisional IRA. Latterly, two of it's splinter groups, the Real IRA and Continuity IRA, have been designated.
the IRA's connections to the PLO, the ANC, Libya and the Soviets.
That last one is also a 'citation needed' affair; the Soviet Union was more aligned with the Official IRA, the other half of the 1969 IRA split, and they, or some Warsaw Pact nation, gave them a small amount of weaponry in the early 1970's. They stopped operations against the British government in 1972, and aren't the group that people would associate with the name 'IRA' these days.
That isn't to say that some people in positions of power may not have thought they were - Claire Sterling wrote an influential book, 'The Terror Network', which did make claims of far-reaching soviet support of terrorism, including the Provisonal IRA, though that's is disputed (some ex-CIA personnel even claim that parts of the book were unintentionally sourced from CIA black propaganda)