In Washington, a heated debate has erupted over immigration. But across the country, the consensus among Democrats and Republicans may be broader than might be expected.

So, how to explain the disconnect? There are several reasons why national harmony over some key ideas doesn't necessarily presage a congressional deal.

First, a look at the numbers. A new Gallup survey released this week shows Americans aren't that far apart when it comes to a handful of key immigration reform proposals under debate on Capitol Hill. Nearly all the proposals receive majority support from both Republicans and Democrats, as the following chart shows.

Those numbers may look pretty good to those hoping a broad reform package can pass. But here's why a deal is far from certain:

1. Congress has shown a willingness to go against the public opinion grain: The just-completed debate over guns is a recent example. Even as polls showed broad support for expanded background checks, complex regional/political considerations doomed the amendment. When it comes to immigration debate, House Republicans from conservative districts will have to be won over. That promises to be a tough sell. As the Cook Report recently illustrated, even many of Republicans from districts with big Hispanic populations are not sure bets to support reform.

2. The whole doesn't always equal the sum of its parts: Respondents were asked about individual provisions in the Gallup poll. That doesn't mean they will be popular when lumped together. Some House Republicans have expressed concerns about passing a "comprehensive" package over a piecemeal approach. The public may be similarly hesitant. A recent CNN/ORC poll asked respondents about the Senate's comprehensive bill, and revealed a divide. Fifty-one percent said they favored it, 45 percent said they opposed it.

3. Rhetoric matters: As we've noted in this space, the language matters. That's true for both the way politicians talk about ideas, and the way poll questions are worded.

Take the "path to citizenship" question. The Gallup poll describes a "long" waiting period and a "criminal" background check tied to the path, strict language that could explain why many Republicans said they would support it. A recent Washington Post-ABC News poll asked if respondents would support a "program giving undocumented immigrants now living in the United States the right to live here legally if they pay a fine and meet other requirements." In that survey, just 42 percent of Republicans supported the idea.

The way the word war plays out in the public conversation will also matter. Conservative critics, for example, will continue to lob allegations of "amnesty" in an effort to scuttle the reform effort.

Sen. Chuck Schumer (D-N.Y.) realizes the importance of words. As detailed in a recent New Yorker story, Schumer realized early on in the current reform effort that using ”undocumented workers" over "illegal immigrants" could backfire among moderates and conservatives.

So, what to make of the overall state of play in the debate as it stands today?

The news on Thursday that key senators have reached a deal on beefing up border security in the Senate bill was a boost for the "Gang of Eight" bipartisan group that crafted the immigration overhaul legislation. So was the nonpartisan Congressional Budget Office's finding earlier this week that the Senate bill would trim deficits by nearly $200 million.

On the other hand, House Speaker John Boehner's vow not to bring a bill to a vote in the House that does not have majority GOP support promises to make it even tougher for a Senate-passed bill to clear the more conservative House.

The bottom line is that the fate of the immigration reform effort remains in doubt -- no matter what the polls say.