Sens. Mark BegichMark Peter BegichFormer Alaska senator jumps into governor race Overnight Energy: Trump directs Perry to stop coal plant closures | EPA spent ,560 on customized pens | EPA viewed postcard to Pruitt as a threat Perez creates advisory team for DNC transition 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 LandrieuLandrieu dynasty faces a pause in Louisiana Senate GOP rejects Trump’s call to go big on gun legislation Project Veritas at risk of losing fundraising license in New York, AG warns MORE (D-La.) hold narrow single-digit leads against their most likely opponents, according to the polls. Rep. Shelley Moore CapitoShelley Wellons Moore CapitoSenate panel advances three spending bills Press shuts out lawmakers to win congressional softball game Senate DHS bill includes .6 billion for ‘fencing’ on border 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.