Sens. Mark BegichMark Peter BegichPerez creates advisory team for DNC transition The future of the Arctic 2016’s battle for the Senate: A shifting map MORE (D-Alaska), Mark PryorMark Lunsford PryorMedicaid rollback looms for GOP senators in 2020 Cotton pitches anti-Democrat message to SC delegation Ex-Sen. Kay Hagan joins lobby firm MORE (D-Ark.) and Mary LandrieuMary Loretta LandrieuSenate GOP rejects Trump’s call to go big on gun legislation Project Veritas at risk of losing fundraising license in New York, AG warns You want to recall John McCain? Good luck, it will be impossible MORE (D-La.) hold narrow single-digit leads against their most likely opponents, according to the polls. Rep. Shelley Moore CapitoShelley Wellons Moore CapitoLawmakers propose boosting park funding with oil money Lawmakers trade barbs, torch Trump at DC soiree Overnight Health Care: Senators unveil bipartisan opioid bill | DOJ to seek reimbursements from opioid companies | Groups looking to end AIDS fear losing ground under Trump MORE (R-W.Va.) holds a solid double-digit lead over her most likely opponent for her state's open seat.

Begich, Landrieu and Pryor all lead their likely opponents by three points or a less, a sign all three will have tough races this fall.

If Begich faces either Alaska Lieutenant Gov. Mead Treadwell (R) or former Alaska Natural Resources Commissioner Dan Sullivan (R) he's in a tight race. But if 2010 Senate nominee Joe Miller (R) wins the primary, a less likely scenario, Begich's lead jumps to a 27-point edge.

The surveys were conducted by the GOP firm Harper Polling in the last week of September, before the government shutdown that has hurt Republicans' numbers nationwide.

A Crossroads spokesman says the group did not poll other top-tier Senate races like Montana and North Carolina. The polling included a primary test showing Capito with a clear lead over her opponents, but the spokesman says they didn't conducted similar surveys on Alaska's GOP primary or test a Tea Party candidate in Louisiana.

This post was updated at 10:40 a.m.