It's a bit hard to answer this on mobile and get all of the links in, but there was quite a bit of controversy around these lay offs. The first was that she ordered the layoffs but reopened the same number of jobs in foreign countries, and in many cases more jobs. The work force of HP actually grew significantly over her tenure, just with cheaper foreign labor.
This is in contrast to Meg Whitman who, during my personal tenure at HP, laid off far more employees than Carly. Meg though did not try to add back head count in a cheaper way. She was just reducing the work force, which was needed. When I started HP had 360,000 employees, post Carly. (Disclosure: I was laid off from HP during a Whitman lay off).
The other thing which made Carly's lay off controversial was that they changed HPs technical ecosystem pretty significantly. For most of HPs history they had been giving employees significant amounts of equity in the company. When Carly came in there were high ranking technologist with quite a bit of voting ability due to their stock holdings. This put a real cramp on the executives ability to make decisions without those pesky engineers using logic to ruin it. When she first came in, for example, she couldn't get board approval to lay people off.
To solve the problem Carly did two things. First she diluted the value of the existing stock by merging with compaq. After that the existing power that the engineers held was diluted enough that she could make the decisions she wanted without as much problem.
This is where the quote having to do with laying people off quicker comes from. She really had to work for those lay offs by restructuring a company first. Another often heard comment from her was that a business as big as HP should never be run or managed by engineers... We have MBAs for that.
She was not well liked.