In the sprint to next Tuesday's US midterm elections, new polls show some besieged Democrats holding their own, complicating the narrative that Republicans are on track to seize the Senate majority.

Alaska in particular bears good news for President Barack Obama's party: two recent surveys show incumbent Senator Mark Begich with a substantial lead, the first polls in a month to put him ahead of Republican challenger Dan Sullivan.

Alaska-based Republican-leaning firm Hellenthal and Associates released a poll Friday putting Begich ahead by 10 points.

Late Monday, Ivan Moore Research group released an October 24-26 poll on Facebook showing Begich with 48.3 percent and Sullivan 41.6 percent.

Polling is unreliable in Alaska, a remote, sparsely populated state with a large percentage of independent voters.

But the results were significant enough for The New York Times to shift Alaska from likely Republican into the "toss-up" column, joining Georgia, Iowa and Kansas.

In Iowa, a Loras College poll of 1,121 registered voters put Democrat Bruce Braley up by one point against conservative Joni Ernst, countering a recent trend showing Ernst ahead in their tight race. A YouGov poll put the pair even at 44 percent.

And in red-leaning Arkansas, under-pressure Democratic Senator Mark Pryor has narrowed the gap to two points against Republican Tom Cotton, 43-45 percent, according to an NBC News/Marist Poll.

However, even if Begich and Braley pull off victories, Democrats face tough math to keep control of the Senate.

They currently hold a 55-45 majority over Republicans, who would need to win a net six seats to win control of the chamber.

Three Democratic seats -- in Montana, South Dakota and West Virginia -- will almost certainly flip Republican, and Obama's underwater favorability numbers with voters is acting as a severe drag on Democrats in battleground states.

Top election forecast models show Democratic incumbents trailing in Arkansas, Colorado and Louisiana, and barely holding on in North Carolina and New Hampshire.

Republicans could face trouble in traditionally red states Georgia, Kansas and Kentucky, where Democrats -- and in the case of Kansas, an independent -- are hoping to pick off one or two seats.