A new Rasmussen poll finds Senator Chuck Grassley’s lead shrinking against Roxanne Conlin and Terry Branstad still over 50 percent against Governor Chet Culver. Rasmussen surveyed 500 Iowa likely voters on April 29, producing a margin of error of plus or minus 4.5 percent.

In the Senate race (survey questions and toplines here), Rasmussen found Grassley ahead of Conlin 53 percent to 40 percent. Grassley led Conlin 55-36 in Rasmussen’s previous Iowa poll, taken in mid-March. Rasmussen’s summary notes that Grassley “now leads Conlin by only five points among women.”

Grassley leads Democrat Bob Krause by 57 percent to 31 percent, the same as in Rasmussen’s March poll. He leads Tom Fiegen by 57 percent to 30 percent, a slightly smaller margin than his 57-28 lead in March.

This race is still Grassley’s to lose; Rasmussen finds 63 percent of respondents have a very or somewhat favorable opinion of the incumbent, while only 34 percent have a very or somewhat unfavorable opinion. The corresponding numbers for Conlin are 44 favorable/30 unfavorable.

However, a few stumbles by Grassley could make this race highly competitive in a hurry. At the very least Conlin is going to make it a lot closer than any other Democrat has against Grassley in the last 25 years.

I expect Conlin to have little trouble winning the Democratic primary on June 8. Not only is she the best-known candidate, she out-raised Grassley in the first quarter and had about $1 million cash on hand as of March 31. According to FEC reports, Krause had $352 and Fiegen had $582 on hand at the end of the first quarter. The Des Moines Register recently profiled Conlin, Fiegen and Krause.

Rasmussen’s numbers on the governor’s race continue to point to a tough road ahead for Culver. He trails Branstad 53 percent to 38 percent, little changed from Branstad’s 52-36 lead in Rasmussen’s March poll. Bob Vander Plaats leads Culver 45-41 in the new poll, up from a 42-40 lead in the March poll. Culver is barely ahead of Rod Roberts in the new poll, 43-41, little changed from the 40-38 lead Culver had against Roberts in the previous poll.

It’s not encouraging for an incumbent to be stuck around 40 percent against all challengers. Culver needs to bring up his own numbers and get out there to tell voters about his administration’s successes. For a preview of the case Culver will make with Iowa voters, watch his appearance on Chuck Todd’s MSNBC program last week.

Assuming Branstad will be the Republican nominee, Culver’s campaign will have to take him on aggressively. The race is bound to tighten up, but as long as Branstad is polling above 50 percent the odds are against Culver. Perhaps the governor can needle Branstad and provoke the same kind of response Vander Plaats got during the second Republican debate.

What do you think, Bleeding Heartland readers?

UPDATE: At Daily Kos, Steve Singiser comments, “is it possible that one of the most invulnerable Senators in recent American history is really within striking range. Looking at the Rasmussen poll in Iowa, it appears so.”