At the moment, it doesn't look like the federal government will shut down at the end of September. While Congress hasn't sent President Obama a funding bill yet, a clean, Democratic-backed proposal broke a Senate filibuster on Monday and appears set to pass the House as well. But the week's relatively smooth sailing was by no means guaranteed.

Before House Speaker John Boehner announced his resignation last week — freeing him up to fund the government with Democratic votes without any fear of backlash from his members — the Republican rank and file was pushing to end funding for Planned Parenthood in the wake of the abortion provider's video scandal. Given that Obama would never sign a funding bill that gutted the organization, a real GOP attempt to defund Planned Parenthood would have almost certainly led to a shutdown. And with the Senate-backed bill only extending funding until December 11, a shutdown could still be coming within a matter of months.

Polling evidence, however, suggests that a shutdown over Planned Parenthood would be a huge strategic error on the part of Republicans. In a poll conducted by Hart Research Associates for NBC News and the Wall Street Journal from September 20 to 24, Planned Parenthood emerged as the most popular political entity, with 16 percent net approval:

The most popular political entity in the new NBC/WSJ poll is ..... Planned Parenthood (like it was in July) pic.twitter.com/o6uST3Z2P6 — Mark Murray (@mmurraypolitics) September 28, 2015

It's more popular than Bernie Sanders, or Barack Obama, or Hillary Clinton, and much, much more popular than the Republican Party as a whole, which has a net approval of negative 16.

A new poll from Pew Research Center also suggests a Planned Parenthood shutdown would backfire. When Pew asked respondents if they'd blame Republicans or Democrats for a shutdown, 14 percent more fingered Republicans:

By contrast, before the October 2013 shutdown, respondents only blamed Republicans over the Obama administration by 3 percentage points. That shutdown is generally remembered as a catastrophe for congressional Republicans. Pew's poll suggests that a Planned Parenthood shutdown could be even worse for the party.

One caveat: Americans' attitudes toward funding abortion providers vary a lot depending on how you phrase the question. Americans have in past surveys been way more receptive to giving funds to Planned Parenthood than to "any organization that also provides abortion"; support for funding Planned Parenthood also drops if respondents are reminded that "an anti-abortion group recently released videos reportedly showing Planned Parenthood staff saying they sell tissue from aborted fetuses."

That said, the relative popularity of the organization compared with just about every prominent politician — and compared with the Republican party as a whole — is striking, and something that should give Republicans hankering for a showdown over funding the group pause.