Conventional political wisdom says House Republicans must oppose comprehensive immigration reform if they want to avoid primary challenges from the right. But do they?

A recent poll conducted by Republican pollsters suggests that the danger may be overblown. According to a survey by Jon Lerner at the Club for Growth, only about 20 percent of likely Republican primary voters are completely against immigration reform and a path to citizenship.

While this group is adept at grabbing the microphone, most of the rest of committed Republicans actually support immigration reform, especially with the caveats and concessions outlined in the Senate's compromise bill.

A full 79 percent of Republican primary voters believe immigration reform is a very important issue that requires a solution, and 78 percent would approve of a solution that didn't give them everything they wanted, if it meant at least something got done.

When asked specifically about the requirements outlined in the Senate bill -- back taxes, a background check, English fluency and a 13-year wait -- 70 percent of respondents were satisfied.

Add that to the fact that the number of Republican incumbents who have been toppled by a more conservative challenger over immigration is virtually nil. Certainly there's been in influx of primary attacks from Tea Party affiliates in recent years, but those tend to center around social issues or tax policy. While immigration may be mentioned, it's rarely the determining factor.

But that's not to say that Republicans have nothing to fear, that there will be no blowback if they pass immigration reform. The Lerner poll was commissioned by FWD.us, the pro-immigration reform lobbying group founded by Facebook CEO Mark Zuckerberg.

That certainly doesn't mean the survey is biased, but they picture likely isn't as rosy as it seems. For one thing, though Republicans voters may support a bill with proposals identical to the Senate's bill, they are more likely to oppose it when packaged as such. Just as most Americans support the individual measures enacted by Obamacare but support falls precipitously once the label "Obamacare" is applied. That is, Republican voters can probably be rallied against "immigration reform" or "amnesty" even if they support the proposals in the bill.

In addition, Tea Party candidates looking to push an anti-tax agenda have already taken the low-hanging fruit in Congress. Future challengers will need another issue to use in attacks on surviving incumbents, and there's a good chance immigration reform will be one of them.

Of course, without immigration reform, Republicans lose any chance at the presidency. Are they willing to make that tradeoff?