Do moderate Republicans matter in the government shutdown fight?

This week the House's conservatives held sway in Republicans' intra-party battles over the government shutdown, despite the talk of moderates who might break ranks: no "clean" budget bill - that is, one that didn't defund Obamacare - came to the floor. And CBS News' whip count showed it was never certain to pass. Many were left wondering where the moderates had gone and why they couldn't exert more leverage.

The simplest answers (often, the best) aren't just about gerrymandered districts or threats of primary challenges, though that's part of it. The simplest answer is that it was conservative voters who put the Republican House majority in power. And you dance with who brung 'ya.

Reason 1: Moderate voters are simply a small part of the Republicans' national coalition -- and possibly getting smaller.

In the 2012 election that brought the current House to office, 60 percent of the Republicans' total House vote nationwide - that is, all the votes cast for them, across all the districts - came from conservative voters, and just 30 percent of Republicans' total votes came from self-described moderates. This was even more pronounced in the wave that brought the GOP into control of the House in 2010, when a full two-thirds of their vote came from conservative voters. Sure, it is tempting to think about moderates as swing voters that provide the edge in swing districts, but the fact is that with so few swing districts, this impact is diminished. This chart is among people who already voted Republican, so if you think about the House as representing those who put them into office - rather than who they're trying to win over - this very lopsided conservative-moderate breakdown tells an important tale.

(For Democrats, if you're wondering, there's less comparison with them and their own ideological base; 43% of their House vote came from liberals. And there are just fewer liberals than conservatives, anyway.)

Reason 2: The representation gap - or - where moderate Republicans are more plentiful, Republican House seats are more scarce.

Moderate voters don't really drive any regional bloc of Republican House members. Even in the northeast, where moderate Republican voters are relatively more plentiful, the party still hasn't won many seats. There are a host of other reasons for these losses but in the end, same result; less representation is less clout.

In 2012, Republican House voters in the east were the most likely of any region to call themselves moderates (39 percent) as one might expect -- but the GOP still doesn't win there. Only 11 percent of their House caucus, or just over two dozen seats, are found in the northeast and Atlantic regions.

By contrast, Republican votes in the south were the least likely of any region to come from moderates (31 percent), and most likely to come from conservatives. Again, as you might expect and this pattern is typical of recent years, including 2010 too, where almost seven in 10 southern Republican House votes came from a conservative voter.

In the south, the GOP wins: more than four in 10 of today's GOP caucus comes from the south; more than four times as many, in percentage terms, as in the east, more than 100 seats of its 232-seat caucus.

Of course, winning general elections is simply easier for Republicans in the south because conservatives are just more numerous in the region, but thinking within the party as it stands today, that gives conservative voters much more voice in the current caucus.

And, conservatives can argue it's their turnout, as much as winning moderates, behind the House majority.

When the GOP has done well of late, they've won a relatively larger share of all moderates, but they also benefitted from more conservatives showing up. In 2010, the banner year Republicans took over the House, there was an uptick (to 42 percent, highest in at least a decade) in total conservatives in the national House electorate.

Reason 3: Moderates want very different things.

Lately these things aren't easy to reconcile, either. In some respects we're just throwing labels around because the disagreements are more over approach to government and legislative tactics than ideology and policy. But there are demonstrated differences in policy preferences, too. In 2012, the moderates who voted Republican were less likely than their conservative partners to call for full repeal of Obamacare: 34 percent did, while 59 percent of the conservative GOP House voters did.

Overall, just 19 percent of GOP-voting moderates voiced support for the tea party movement at the ballot box last year; 52 percent of conservatives did. That immediately puts those moderate voters in a very different place than the members whose rise and backing came very directly from tea party groups and support.

Today, when we look at reaction to the shutdown within Republican-held districts, and within swing districts, and we see more displeasure among moderates. Moderates who live in Republican-held districts have, in our recent CBS News and CBS News/NY Times polling, tended to blame or say they would blame Republicans for the shutdown, slightly more than they blame President Obama. (Note that this is of course in flux, and this is combined interviews done over the days leading into and just after the shutdown. It's an indicator, not a final verdict.)

And if we look across the districts by their partisanship rankings (whether the district leans Republican or Democrat, or is mixed) we see that moderates who live in swing districts are much the same way - they were leaning toward blame for the GOP. This is also true of moderates who live in Republican-held districts (and very much the case among those living in Democratic-held districts.)

So it isn't news when we say the Republican Party is a conservative party.

When looking at the House and how it operates, it's also important to remember that accountability runs both backward and forward in time: think in terms of who send Republicans to the House in the first place. They owe their majority very much to conservatives.

It is far, far too soon to say whether this may have impact next year, and it remains true that Republicans have an edge to keep the House. Nor should moderates automatically be assumed to be, or confused with, swing voters; nor do we have any evidence they're abandoning Republicans yet. That does not, however, mean the party can only appeal to conservatives and be assured of keeping the House, and certainly not if they want to grow it. If you want to keep tabs on the impact of this shutdown for the party, start by watching the moderates.

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    Anthony Salvanto is CBS News elections director