Republicans rejected those, and "offered their own versions" of the legislation that included mandatory minimum sentences. "However, advocates of domestic violence awareness were specifically against the inclusion of these provisions," Politifact notes. They "worried that long mandatory minimums would 'keep victims who were assaulted by someone they know from reporting' and would create other issues in sentencing."
Politifact's ruling boiled down to this: "McConnell could argue that the mandatory minimum sentences Republicans required in their alternative made for a 'stronger' bill, but advocates of domestic abuse awareness opposed this measure as unnecessary. And the Republican measure was absent several protections for certain groups that were included in the bill Obama signed. McConnell is within his right to oppose those provisions, but it makes it hard for him to prove that he supported 'stronger' legislation."
As for the Grimes ad to which McConnell is responding, Politifact rated it half true, "given McConnell's history of voting for the act at times." His ad notes that he was an original sponsor of the act -- one of only three Republicans, Politifact noted. He didn't sponsor the first version that passed, but voted for it as part of another bill. He voted against the final version, which included provisions added by the House, including "a much more controversial assault-weapons ban," Politifact says. It also cites an analysis of the ad by FactCheck, which was reported in this blog last week.