Collins said Tuesday morning that he's received phone calls, texts and emails, as well as messages on Facebook and Twitter, and has been spending time "just trying to thank everyone for their support."
The 7-footer said one of the most meaningful messages was a text Monday night from King, the former tennis great
"She just got back from Sochi. With all that's happening with the loss of her mother, she was great. It was really nice to hear from her. It was very meaningful and very much appreciated," Collins said.
King and two other openly gay athletes—Brian Boitano and Caitlin Cahow—were selected for President Barack Obama's official U.S. delegation for the opening ceremony of the Sochi Olympics, but King delayed her trip because of her mother's death. She attended the closing ceremony on Sunday.
Collins signed a 10-day contract on Sunday and played 10 scoreless minutes in a victory against the Los Angeles Lakers.
He revealed at the end of last season that he is gay, but was a free agent and had remained unsigned until the Nets needed another big man.
The 35-year-old center said there have been a few "crazies" on Twitter, but added: "I've always done a good job of just blocking those people immediately and never responding.
"As far as people who have my number, the support has been overwhelming."
Collins spoke briefly with reporters before the Nets practiced at UCLA on Tuesday morning. They resume their road trip with a game at Portland on Wednesday night.
At one point he was practically drowned out by the clatter of a dozen or so basketballs bouncing on the hardwood at the Student Activities Center as his teammates began warming up.
It was a reminder of why Collins is with the Nets.
"I'm just trying to prioritize things. Basketball right now is a priority," he said. "Again, it's about the plays, our calls, trying to get comfortable with just what it is the Brooklyn Nets do on both ends of the court."
Collins said he was glad things happened quickly Sunday. He was signed to a contract in the morning, attended a breakfast team meeting and then played that evening.
"That way there was no buildup," he said. "It is what it is and you can start to move on and start to focus on the basketball stuff."
For Collins, that's doing a lot of grunt work.
"Being big, using my size and strength, setting screens and going out there and hitting somebody on both ends of the court," he said.
Guard Deron Williams chuckled about Collins getting five fouls on Sunday night.
"Jason is solid. He sets screens, plays hard, uses his fouls wisely. We were joking that he's a professional fouler. He used five fouls wisely," Williams said. "He did a good job."
Williams also talked about how bad Collins' golf game is.
"It's almost like Charles Barkley. It's pretty bad," he said.
With a need for another big man, the Nets turned to Collins, who helped them reach two NBA Finals in the early 2000s.
General manager Billy King said on Sunday that it was a basketball decision.
"He's another basketball player helping our team win. That's all it is. It doesn't matter. We've got so many guys who've known him for years, have played with him. I've known him. So nothing changes."
Still, Williams said Sunday night was a big deal.
"He's showed a lot of courage in coming out and being open with it," Williams said. "We're happy for him and glad to have him on board. It's big to be a part of it. It's definitely historic for him to come out here and play, the first openly gay athlete to play in a major sport. It's definitely a big deal. We know there's going to be a lot of media, a lot of questions about him every day, but rightfully so. But hopefully him doing this, and Michael Sam, eventually it will be the norm. It won't be a big deal."
Sam is the SEC co-defensive player of the year from Missouri who recently revealed he is gay. His on-field workouts at the NFL combine in Indianapolis were on Monday.
Collins said it's up to the media to decide when the story is less about him being an openly gay player and more about him just being a basketball player.
"There's only so many ways you can talk about the off-court stuff until really the focus is on basketball and how the team is doing," he said.
Asked about the pressure of being under a 10-day contract, Collins said: "I don't think I really have to, at this point in my career, prove myself. Most of the guys know what I can do. The key thing is just being in shape, which I am."
Is he anxious?
"There's a lot in life you can worry about. That's not one of them," he said.
Follow Bernie Wilson on Twitter at http://twitter.com/berniewilson