That's the point. If the Democrats block it, they look disingenuous and partisan (moreso) at the expense of the common person. If they vote for it and it passes, the GOP takes credit for helping to fix a major problem with Obamacare.
I think the GOP is betting that the Democrats are not going to turn their backs on Obama and actually concede that they lied to and misled the American public, so that GOP can say next year that they tried to uphold the promise that you could keep your healthcare, but the Democrats and Obama blocked it.