Yes, that's about what Barr said, but I don't think it's gonna turn out that way.
Why did the Congress give Barr an arbitrary deadline? He has said he will release it in mid-April or before. It's a long report and there is stuff in there that no doubt needs to be redacted by law. So giving him a few weeks is not unreasonable.
What is happening on April 3 that makes the Congress's deadline so important?
There is nothing special about April 3.
Why Congress moves, and tries to move swiftly, is impossible to tell, for none of us have direct access to their brains.
On the other hand, we've seen the pervasive "Complete and Total Exoneration" narrative doled out by the shipload. So, it'd be understandable House Democrats would like to move as early as possible to counter that narrative, before it's fixed and unalterable in the national consciousness.
Of course, making Republicans stand up against transparency may be another issue.
In the end, it comes down to trust, or rather, the lack thereof. Trump promised his tax returns for all to see. Remember what happened to that? He then promised the Mueller report, and now they seem to dig in for as long as possible. Meanwhile, Trump moved the narrative again, calling demands for the report a "disgrace". Now, why would Trump call efforts to see the report that completely exonerates him - or so he tells us - a "disgrace"? Funny, no?
Yes, of course, the AG is supposed to follow "the law". The notion the law is somehow simple, offers two-bit answers to the question what is to be published, and what not, is, well, simple, and things may well boil down to how extensive, or narrow, Barr interprets the law on behalf of Trump, and the longer he has, the more elaborate and extensive his redactions might become. So there would be another reason to move early. And yes, there is another, entirely novel thing at work, and I'll coin "Congressional Grandstanding" to describe it. Never seen that one before...