Kaine is not as liberal as some Democrats would prefer on a range of issues, most prominently trade and abortion rights.
Two major labor groups praised him despite his support for the Trans-Pacific Partnership. AFL-CIO President Richard Trumka said Kaine had a "strong record on workers' issues" and proclaimed him a "winner for America." The SEIU also praised Kaine's record as well, saying, "We know what is in Tim Kaine's heart."
But two other progressive groups, however, the Progressive Change Campaign Committee and Democracy for America, took issue with the choice, citing Kaine's support for the TPP, a massive 12-nation Pacific rim trade deal opposed by progressives.
"Since Tim Kaine voted to fast track the Trans-Pacific Partnership, Republicans now have a new opening to attack Democrats on this economic populist issue," the PCCC said in a statement. "The mood of the country is a populist one. The center of gravity in the Democratic Party has shifted in a bold, populist, progressive direction -- regardless of who is selected by Hillary Clinton as vice president."
Democracy for America executive director Charles Chamberlain said Clinton's choice would present challenges for his group's advocacy against Donald Trump.
"Secretary Clinton's choice of Senator Tim Kaine as her running mate doesn't change that goal, but Kaine's support for fast-track authority for the job-killing Trans-Pacific Partnership and recent backing of bank deregulation will make our work more difficult," he wrote in a statement.
Two major groups that favor abortion rights chose not to criticize Kaine, with the National Association for the Repeal of Abortion Laws noting his legislative record.
"While Senator Kaine has been open about his personal reservations abut abortion, he's maintained a 100% pro-choice voting record in the US Senate," the group said in a statement. "When he was governor, Tim Kaine took positions we disagreed with and actively campaigned against. We're pleased that since then, his votes and public statements have been consistently in favor of trusting women to make our own decisions."
Planned Parenthood also noted his 100% rating on their scorecard, calling him a "thoughtful running mate with integrity."
Minnesota Democratic Sen. Amy Klobuchar told CNN that she thought Kaine was an excellent choice because of his experience, temperament and bipartisan appeal.
"He's just someone that Republicans have a lot of respect for," she told Don Lemon on "CNN Tonight." "He's someone who takes responsibility for things. You saw that when he was mayor (of Richmond), when he was governor."
Republicans, meanwhile, labeled Kaine a Washington insider.
In a fundraising text message to supporters, Trump's campaign wrote: "The ultimate insiders -- Obama, Hillary and Kaine. Don't Let Obama have a 3rd Term. Contribute."
The campaign later issued a lengthy statement, labeling the Virginia Democrat "corrupt Kaine."
"It's only fitting that Hillary Clinton would select an ethically challenged insider like Tim Kaine who's personally benefited from the rigged system," spokesman Jason Miller said. "While serving in government, Kaine has taken tens of thousands of dollars in freebies -- more than $160,000 in fact -- on free vacations, free clothes, and free tickets. If you think Crooked Hillary and Corrupt Kaine are going to change anything in Washington, it's just the opposite."
Miller was likely referring to Kaine's acceptance of more than $160,000 in gifts
during his time as governor, benefiting from Virginia's loose laws related to political gift giving. There was no accusation, however, that Kaine helped any of his gift givers through his official capacity as governor.
Trump himself picked up on that line of attack Friday night, tweeting, "Is it the same Kaine that took hundreds of thousands of dollars in gifts while Governor of Virginia and didn't get indicted while Bob M did?" Trump tweeted, referring to Kaine's successor, Bob McDonnell.
Kaine spokeswoman Amy Dudley refuted the allegations of impropriety.
"During his eight years as lieutenant governor and governor, Senator Kaine went beyond the requirements of Virginia law, promptly disclosing any and all gifts received, including those beneath the reporting threshold," Dudley said in a statement. "All disclosure information -- the vast majority of which was for work-related travel expenses rather than gifts -- has been publicly available for years and never once raised any concerns of impropriety."
Anti-Trump Republicans praise Kaine
Meanwhile, the Republican National Committee tried to stoke tensions between Clinton and the liberal base that initially flocked to Bernie Sanders, saying that Kaine did "nothing to unify a fractured Democrat base which is repelled by her dishonesty and cronyism."
Two prominent critics of the Trump, though, tweeted some support for their Senate colleague.
Jeff Flake, an Arizona Republican, wrote: "Trying to count the ways I hate @timkaine. Drawing a blank. Congrats to a good man and a good friend."
And Lindsey Graham, another Trump critic, tweeted: "I find the VP candidates -- Governor Mike Pence and Senator Tim Kaine -- more palatable than the presidential nominees."
Even hip-hop artist MC Hammer, best known for hit songs "U Can't Touch This" and "2 Legit 2 Quit," weighed in on the choice.
He tweeted Friday, "Tim Kaine is an excellent choice !!! Good man. Here with my Brother Raul Fernandez. #ClintonKaine"
The tweet included a photo of Kaine with the musician and entrepreneur Raul Fernandez at a Washington Capitals game.
Other Clinton VP candidates react
Several other names floated to be Clinton's running mate praised Clinton's choice.
New Jersey Sen. Cory Booker quickly praised Kaine.
His first tweet came right after the announcement, when he tweeted, "KAINE IS ABLE!!!" which is a biblical reference to the story of Cain and Abel.
He added, "Sincerely, Tim Kaine is 1 of the most honorable men in politics. I admire & am inspired by him, give them your vote."
Colorado Gov. John Hickenlooper tweeted congratulations to Kaine.
"Great choice @HillaryClinton. @TimKaine is one of America's hardest working, optimistic, experienced public servants," he tweeted.
And Labor Secretary Tom Perez told CNN that Kaine is "a great man."
"The first conversation I ever had with Tim Kaine was about our shared love of civil rights law and fair housing policy," he said in a statement. "He is a great man, he will make an even better vice president, and as a proud progressive, I cannot wait to vote for him in November."