A representative for families of the Newtown shooting victims has asked Senator Mitch McConnell to hold a meeting with them, according to sources familiar with the request. McConnell’s office initially declined the request on the basis of scheduling, a source says — and now family members are set to call McConnell and reiterate the request personally.

How will McConnell respond?

The request – if granted — would allow the families to come face to face with the primary architect of the GOP’s strategy of blocking everything Dems propose to slow the tide of gun violence. If it is denied, it would be a big story, and could lend support to the argument that Republicans are callously rebuffing the families — and prioritizing the gun lobby over them – in the wake of a massacre that claimed the lives of 20 Newtown children.

The request — which was made by a representative of Sandy Hook Promise, a group that includes around a dozen family members who are lobbying Washington lawmakers – represents something of a shift in strategy by the families, and carries interesting implications for later stages in this battle. Previously, the families, who had met with many Democratic and Republican Senators, had shied away from asking for a meeting with McConnell, on the theory that they should focus their energy on Senators they deemed persuadable. This irritated Democrats who wanted to see more public pressure put on their GOP counterparts.

But now the families are asking McConnell for a meeting. The families are not optimistic that the meeting will move McConnell, a source familiar with their thinking says, but this will placate Dems who want public pressure put on the leader of Senate Republicans. What’s more, if the legislation fails, the families don’t want to be in the position of retrospectively wondering if they had done all they could to get it passed, particularly since a round of bitter finger-pointing would be all but inevitable. And finally, the source says, the families are hoping to initiate a longer term conversation — one beyond the current battle – with even hostile lawmakers about other ways of combatting gun violence, such as school safety and addressing mental illness.

Asked for comment, McConnell spokesman John Ashbrook emailed me this:

Our office recently sat down with folks from Newtown for a lengthy discussion and we’re certainly open to doing it again. We actually offered another meeting and are waiting to hear back.

It’s unclear which Newtown residents this refers to or whether McConnell is willing to meet personally with families.

There’s another angle worth considering here, too. While McConnell obviously wants to sink the Manchin-Toomey background check proposal via procedural means — whether by filibuster or by voting it down as an amendment, which would require 60 votes to pass – Democrats and gun control advocates believe he wants a few red state Dems to oppose it in the procedural vote, too. That would mean that the proposal was blocked by a bipartisan group of Senators — insulating the GOP from some blame — as opposed to meaning it was defeated solely by Republicans who were determined to avoid allowing it come to a simple majority vote.

If the families put more pressure on McConnell, it won’t move him, but it could perhaps make it tougher politically for the GOP alone to sink the proposal. And so, if the remaining hold out red state Dems ultimately do support moving the bill forward past the next supermajority procedural vote, it would then become harder for the remaining Republican holdouts — Kelly Ayotte and Dean Heller — to vote No, because then the blame for killing the whole proposal by procedural means would fall on the GOP.

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UPDATE: Post edited slightly for clarity.

Greg Sargent writes The Plum Line blog, a reported opinion blog with a liberal slant -- what you might call “opinionated reporting” from the left.