Posted Wednesday, October 17, 2012 --- 1:05 p.m.

MADISON, Wis. (AP) -- Despite Wisconsin's recent conservative swing, one of the most liberal members of Congress is now locked in a tight race with a well-known Republican for the state's open Senate seat.

Democrat Tammy Baldwin is providing a tough challenge to former Republican Gov. Tommy Thompson. Allies of both are pouring millions of dollars into the race. Karl Rove's group alone has spent $5 million on television ads attacking Baldwin.

A poll released Wednesday by Marquette University Law School shows the race is a dead heat. Thompson led 46 percent to 45 percent, but that was within the poll's 3.4 percentage point margin of error.

The seat is open due to the retirement of Democratic Sen. Herb Kohl.

Copyright 2012. The Associated Press.