(CNN) Rep. Marsha Blackburn's support for a drug law that she acknowledged might have caused "unintended consequences" is marring her entry into Tennessee's Senate race -- with her Democratic opponent saying she should drop out and potentially stronger foes in both parties now more seriously considering entering the contest.

Blackburn, who last week launched her bid for the retiring Sen. Bob Corker's seat, co-sponsored the measure that was the subject of Sunday's blockbuster investigation by "60 Minutes" and The Washington Post. The Blackburn-backed law, whistleblowers said, made it easier for drug companies to distribute opioids across American communities and thwart the Drug Enforcement Agency.

Already, the lead sponsor of that bill, Pennsylvania Republican Rep. Tom Marino, who took nearly $100,000 in campaign contributions from pharmaceutical interests, has withdrawn as President Donald Trump's nominee to be the nation's drug czar. Marino and Blackburn asked a government watchdog to investigate a DEA official who warned them in 2014 that their bill would aid criminals, accusing the official of intimidation.

In Tennessee, Blackburn is under fire from the left and the right for her role in shepherding the bill through the House and Senate before former President Barack Obama signed it into law.

The top Democratic Senate candidate, military veteran James Mackler, called on Blackburn to withdraw from the race.

"That Congresswoman Blackburn would champion legislation like this while Tennesseans face an opioid epidemic is all one needs to know about her priorities," Mackler said. "The 'unintended consequences' of her legislative actions are that Tennesseans died and she should be held accountable."

And the top potential Democratic recruit, 74-year-old former Nashville mayor and governor Phil Bredesen , told local newspapers he is considering entering the race -- a big shift from his previous insistence that he would not.

A potential Blackburn foe in the Republican primary, former Rep. Stephen Fincher, also blasted the congresswoman for her involvement in the drug bill.

"This goes right to the heart of why we are probably going to get into the race," Fincher told The Tennessean. "This is an issue that shows Tennesseans ... want someone to stand up against special interests."

Blackburn's spokesman -- who asked not to be identified by name -- said any "unintended consequences" from the bill should be "addressed immediately."

"Congressman Blackburn has a long history of working to combat the epidemic of opioid abuse, which has taken too many precious lives," the spokesman said via email. "She believes that Congress should continue its work to address the issue and conduct oversight. If there are unintended consequences from this bipartisan legislation -- which was passed unanimously by the House, Senate and was signed into law by President Obama -- they should be addressed immediately."

Other races could be impacted

The damage could extend beyond Marino's nomination and Blackburn's Senate race.

Three other Republicans who are along Democrats' top targets in the 2018 midterms -- Reps. Mike Coffman of Colorado, Ryan Costello of Pennsylvania and George Holding of North Carolina -- were all at times co-sponsors of Marino's bill.

Costello, according to the Center for Responsive Politics, received $159,200 from pharmaceutical and health product interests during the 2016 campaign cycle.

In a statement, Costello said he and others are evaluating whether the law is working.

"The legislation's clear and stated intent was to have the DEA and distribution companies establish a clear understanding of enforcement standards, allowing for greater collaboration among stakeholders to address modern challenges to prescription drug abuse while still allowing patients with medical needs to have reasonable access," he said. "If the purpose of the law is now not being realized, then we need to fix it. I am in the process of investigating and evaluating this as we speak. I believe many others are as well, especially given it was unanimously supported by the entire Congress and signed into law by President Obama."