Politicians love to claim the American public is on their side, and President Obama is perhaps as fond as anyone of this tack.

On Monday, he did it again, complaining that House Republicans are thwarting the public's will in pulling the plug on immigration legislation this year:

That's what the Senate bill would fix if the House allowed it to go to a vote. Our country and our economy would be stronger today if House Republicans had allowed a simple yes-or-no vote on this bill or, for that matter, any bill. They'd be following the will of the majority of the American people, who support reform.

Obama's claim has merit: Public polls conducted since 2013 have found support for providing illegal immigrants a pathway to legal status ranging from 46 to 81 percent for, cresting above a majority in 13 of 15 polls. But the 35-point range between the most favorable poll and the least favorable one raises some serious questions about how stable or real that support actually is.

So what's going on?

Question wording varies widely across surveys and explains much of the difference. It also reveals a key element of public opinion on immigration: Americans are increasingly supportive of a path to legal status if undocumented immigrants face more requirements. The spreadsheet below shows results for 15 public polls along with their question wording and links to the full surveys.

We counted the number of requirements mentioned in each question to test whether it is related to support. In the three polls showing the highest support for a path to citizenship (CNN/ORC, Fox News and CBS), the survey question mentions between three and five requirements, including criminal background checks, paying back taxes, a waiting period and fines. Polls showing the lowest support do not mention any requirements for immigrants seeking legal status. The statistical correlation (a.k.a.. connection) between a poll's number of immigrant requirements and support for a path to legal status is 0.74 on a scale of 0 to 1 -- with 1 representing a perfect positive relationship.

The Senate law includes all of these requirements for citizenship – and more. The law passed last year lays out a 13-year process, featuring fines, payment of back taxes, regular employment as well as learning English and civics. Given support tends to increase with requirements, the Senate’s proposed route for undocumented immigrants figures to be overwhelmingly popular.

Other elements of the law also gain wide public support. A Gallup poll last June found over seven in 10 saying they’d “vote for” increased border security, allowing foreign science and engineering students to remain in the U.S. to work and requiring business owners to check the immigration status of employees they hire. Smaller majorities supported allowing employers to hire immigrants for jobs Americans don’t want and varying the number of immigrants depending on economic conditions.

So if public support is so clear, why have House Republicans dragged their feet on endorsing the Senate’s bill?

For one, the pockets of opposition to immigration legislation are concentrated within the Republican Party, including some if its most conservative adherents. Surveys find most Republicans support a path to citizenship if undocumented immigrants meet several requirements, but voting for any such law risks accusations of giving amnesty to those who immigrated illegally.

Secondly, voters are not nearly as upset as Obama about failed immigration legislation, and they don’t appear willing to reward pro-immigration reform candidates. A Washington Post-ABC News poll last year following the Senate bill's passage found only 13 percent of Americans said they’d be “angry” if the House didn’t approve a path to citizenship.

Asked how it would impact their vote, a March Post-ABC poll showed 38 percent said they’d be “less likely” to support a candidate for Congress who supports a path to citizenship for undocumented immigrants. Slightly fewer, 30 percent, said they’d be “more likely” to support such a candidate. Among Republicans, 60 percent said they’d be less likely to vote for a candidate who supported a path to citizenship.

Whatever risks exist for national Republicans in alienating Hispanic voters in future elections, the math is clear for an individual member worried about his or her reelection -- and that's only bolstered by the fact Obama is also taking plenty of blame for the lack of progress on immigration.

Obama seemed to acknowledge the problem Monday: "Much of this only happens if Americans continue to push Congress to get this done."

The problem for Obama is that they're not really pushing Congress to get this done even as we speak.

Peyton M. Craighill contributed to this report.