I think not much. Why not?
Obama may not want to bring up this law because, despite the Supreme Court decision, it remains widely unpopular.
Romney may not want to bring it up either. That’s because the Obama campaign would very likely not respond on the issue, but instead would respond by claiming "Romneycare" in Massachusetts was the model for Obamacare. That’s false; Romney’s actual proposal was less intrusive and less expensive than the law that was ultimately enacted in Massachusetts. But, nevertheless:
(1) the explanation is complicated, and would not sway many votes. That’s because most voters would ignore it just because it’s complex.
(2) Worse, it would be a diversion, taking limited debate time away from focusing on Obama’s main governing failures – his wretched economy and his wretched foreign policy.
For these reasons, neither candidate may see much use in bringing up Obamacare; in fact both candidates may see potential harm in doing so. That’s why I think Obamacare will not figure importantly in the debates.
The Romney proposal included an employer mandate that required only catastrophic coverage, not the comprehensive and expensive "Cadillac plan" coverage that was ultimately included in the Massachusetts law, and in ObamaCare.
So, clearly, the Obama plan did not follow the Romney “model” in this feature – a feature important enough that it was disputed all the way to the Supreme Court. There's more:
Romney's successor, Governor Deval Patrick, greatly increased the mandated level of coverage while implementing the law
Deval's tinkering resulted in much higher costs not contemplated in the original law, and those costs still adversely affect the state’s finances. Yet the whole thing is tagged as “Romneycare”. Go figure.
A further insight, which both the linked articles report: On the day that Romneycare was signed into law, Romney line-item-vetoed eight elements changed in or added into the final draft of the bill . . . After the signing ceremony, though, the Democrat legislature returned to the State House and overrode all eight vetoes. (in fact, during 2006 alone, Romney's last year as Governor, Romney issued 250 vetoes, every single one of which was overridden.)
. . . see how easily an Obamacare discussion leads away from the economy and foreign policy? My bet - Romney won't go there - and neither will Obama.