Mitt Romney’s strategy once seemed self-evident. First, skewer President Obama over the tepid economic recovery. Second, lean just enough to the center over the course of the fall campaign so you won’t lose because of social issues, temperament and tone, controversial proposals about the welfare state or other things that might distract voters from your economic message.

With his selection of Representative Paul D. Ryan of Wisconsin as his running mate this month, however, Mr. Romney seems to have been pursuing a different approach, one that focuses more on turning out the Republican base.

Political messaging isn’t a simple matter, and skilled political candidates can develop pitches that resonate with different audiences. In 2008, Mr. Obama simultaneously tried to brand himself as a “post-partisan” moderate, while also seeking to demonstrate to Democratic primary voters that he’d be more reliably liberal than Hillary Rodham Clinton.

But Mr. Romney is probably a less dexterous politician than Mr. Obama. In his acceptance speech before the Republican National Convention on Thursday night, he will probably have to tip his hand as to which goal will be receiving the most emphasis over the balance of his campaign. Will it be a speech designed to fire up the delegates in the room — and the Republican partisans who are watching on Fox News and other networks? Or more one designed to appeal to the independent voters who might be casually flipping through their cable lineups?

The argument for a base strategy is something like this: there are very few undecided voters left, and hardly anything has moved the polls. With the election being so close, the contest will come down to turnout. So get your voters as motivated as possible.

A risk for Mr. Romney, however, is that even with a favorable turnout, the Republican coalition may have become slightly too narrow for him to win, given that the party is struggling with Hispanics and other minority voters.

The pair of charts below reflect the racial voting breakdowns in 2004 and 2008, according to the national exit polls in those years. (I have made very slight adjustments to the numbers so that when you sum up the rows, they exactly match the overall percentage of the popular vote received by each candidate.)

In 2008, Mr. Obama benefited from minority voters in two ways. First, they turned out in greater numbers, making up about 26 percent of the electorate rather than 23 percent in 2004.

But what was more important is simply that a higher share of the minorities who did turn out to vote picked Mr. Obama as their candidate. His share of the nonwhite vote improved to 80 percent from Mr. Kerry’s 71 percent. By contrast, his share of the white vote was only marginally better than Mr. Kerry’s: about 43 percent rather than 41 percent.

It is easy to demonstrate that getting a higher proportion of minority votes was more critical to Mr. Obama’s success than the turnout itself. Let’s run through a couple of quick, hypothetical examples.

First, imagine that the proportion of voters in each racial category who voted Democratic or Republican was the same as in 2004 — but that turnout was the same as in 2008:

Increased minority turnout alone would not have been enough to give the Democrat the election. Instead, it would have been virtually tied, with each side receiving about 49.5 percent of the vote.

Next, consider the opposite case. Turnout looks just like 2004, with a smaller share of minority voters than in 2008. However, the vote split within each racial category follows the 2008 norms, with white voters moving slightly to the Democrat, and minority voters more strongly so. This is enough to give the Democrat a fairly clear win, by about four or five percentage points in the national popular vote:

Of course, Mr. Obama’s share of the white vote will probably not be as strong this year as it was in 2008 (when it wasn’t all that strong to begin with). There is also evidence that the Republican base is more motivated to vote than the Democratic one.

So suppose that the turnout demographics this year look like 2004, when 77 percent of the electorate was white. Furthermore, suppose that Mr. Romney receives the same proportion of the white vote that George W. Bush did in 2004.

However, we’ll assume that Mr. Obama does retain one advantage from 2008. Although fewer minorities turn out, those that do vote for him in the same proportions as 2008, meaning that he gets about 95 percent of the African-American vote, and about two-thirds of the vote from Hispanics, Asians and other racial minorities.

These assumptions yield a very close election — but Mr. Obama wins the popular vote. Specifically, he wins it by about 1.7 percentage points.

Interestingly, that is almost exactly the margin by which Mr. Obama leads Mr. Romney among surveys of likely voters right now.

This may not be a coincidence. The consensus of polls suggests that minority turnout may be down a bit from 2008. It also suggests that Mr. Romney should improve on Mr. McCain’s numbers among white voters. However, the surveys show Mr. Romney struggling with minority voters — including Hispanics, among whom Mr. Obama maintains about a two-to-one advantage in recent surveys.

Turning out your base may not be a sufficient strategy if your base has become too narrow. In 2004, Mr. Bush had an excellent base turnout — but he also captured about 40 percent or 45 percent of the Hispanic vote, a share that Mr. Romney is unlikely to reach. Without that relatively strong performance among Hispanics, the election would have been a tossup.

None of this, obviously, is an absolute constraint. If Mr. Romney not just matches but exceeds Mr. Bush’s 2004 performance among white voters, a base turnout strategy could be enough for him to win.

But pay attention during Thursday night’s speech to whether Mr. Romney offers any moderation on issues like immigration. Otherwise, he may have drawn a very narrow path for himself between now and November.