Donald Trump continues to hold leads in New Hampshire and South Carolina, but Sen. Ted Cruz has grabbed a lead over the real estate mogul in Iowa, according to a poll released Sunday.

In the new CBS News/YouGov battleground poll, Cruz hit the 40 percent marker, topping Trump's 31 percent and dwarfing the rest of the GOP field in the Hawkeye state with 43 days left until the Iowa caucuses. Cruz also leads the Washington Examiner's presidential power rankings.

Over the past month, Cruz's support in the state has nearly doubled. He held 21 percent support in mid-November. Trump, by constrast, is treading water. He also pulled 30 percent support in the previous poll.

Meanwhile, Dr. Ben Carson's standing in the state continues to falter. Carson has fallen from 19 percent and second place to six percent and fourth. Florida Sen. Marco Rubio occupies the third slot with 12 percent backing.

Elsewhere, Trump continues to dominate in the early primary states. He leads in New Hampshire and South Carolina with 32 and 38 percent support, respectively. Cruz runs second in both, with 14 percent in New Hampshire and 23 percent in South Carolina.

Rubio grabs the third spot also in both states, with 13 in New Hampshire and 12 percent in South Carolina.