A group founded by astronaut Mark Kelly and his wife Gabby Giffords -- the former Arizona Congresswoman who was shot in an Arizona shopping plaza in 2011 -- are rolling out a six-figure TV and digital ad campaign in Minnesota this week.

The campaign by Americans for Responsible Solutions in 13 competitive legislative districts will seek to elect candidates who would agree to extend background checks to private sales, gun shows and Internet purchases.  

The digital campaign started last week, while TV in four legislative races will begin Wednesday, including in House District 44a, currently held by Rep. Sarah Anderson, R-Plymouth, who has previously voted against background checks. Her opponent is Ginny Klevorn, a supporter of background checks.

Some DFL lawmakers introduced background checks legislation this year and in 2015 but were rebuffed by a coalition of Republicans and outstate DFLers for whom gun rights are a cherished principle. 

Giffords visited Minnesota last month in an attempt to rally suburban voters. 

A separate effort by Everytown for Gun Safety and Moms Demand Action is also pouring money and volunteers into electing candidates who favor background checks for all sales. 

Gun rights groups and voters, who have traditionally been a sought-after constituency, say their opponents are trying to limit the constitutional rights of gun owners. They say the effort to extend background checks is a trojan horse for a more ambitious gun control agenda. 

The fate of gun rights legislation could rest in the hands of a few thousand voters Nov. 8 as Republicans try to hang on to their MN House majority by preventing the DFL from picking up seven seats. Many of the most vulnerable GOP incumbents are, like Anderson, in the suburbs, where gun control legislation is thought to have the most sway.