But it appears Marshall's defeat of Democratic challenger Cal Cunningham in the Primary runoff on Tuesday has given her a significant bounce.
Rasmussen said Thursday a new poll shows Burr with just 44 percent to Marshall's 43 percent. Considering a margin of error of 4.5 percent, the candidates are in a statistical dead heat.
The poll of 500 likely North Carolina voters was done June 22.
The new numbers may mean a significant boost for Marshall's ability to raise campaign money. Burr has already amassed some $5 million in cash for his campaign while Marshall recently reported having just $200,000 on hand.