Sen. Charles Grassley (R-Iowa) has joined Iowa Gov. Terry Branstad (R) in suggesting it might be time to shutter the Iowa Straw Poll.

Grassley, who had previously declined to weigh in on the issue, told BuzzFeed's John Stanton that one way the state could keep its first-in-the-nation status would be to "maybe not have the straw poll."

Branstad shocked many in the state in November by calling for an end to the straw poll, saying it had "outlived its usefulness."

Many outside the state have suggested the straw poll isn't a good use of resources or time, and they note that several top-tier candidates have opted to skip it in recent years. Rep. Michele Bachmann's (R-Minn.) 2011 straw poll win was seen as perhaps the nail in the coffin -- especially considering she wound up finishing a distant sixth in the state's caucuses.

Rep. Michele Bachmann (R-Minn.). (Chris Carlson - AP)

(Fun fact: Bachmann got nearly as many votes at the straw poll -- attended by 17,000 people -- as she did in the caucuses -- in which more than 120,000 people voted.)

But within Iowa, the straw poll remains a big fundraiser for the state GOP, which means it will be hard to give up. Shortly after Branstad's comments, a majority of state central committee members voted to keep the straw poll.

But the majority was slim, which suggests support for the straw poll is dropping.

The first straw poll was held in 1979.