The president of the Koch brothers-funded political group Americans for Prosperity (AFP) is irked by the the Republican efforts to repeal and replace Obamacare.

AFP president Tim Phillips feels that GOP lawmakers in both the House, and now, the Senate, are pushing legislation that simply doesn't go far enough.

"Maybe we were naïve, Major. Maybe we were just naïve," he told CBS News Chief White House Correspondent Major Garrett on "The Takeout" podcast, which was recorded before the Senate bill was released. "But we thought that when you promised in four consecutive election cycles -- we thought maybe that would be the time to keep your word," Phillips said.

Republicans have gone back on a promise they made seven years ago, during the 2010 midterms to repeal Obamacare, Phillips told Garrett, and that was the promise that propelled them to a majority in the House.

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House Republicans "didn't do it" with their repeal-and-replace bill passed last month, said Phillips. "That was disappointing, deeply disappointing."

"What we're telling Republicans is this: If you pass something, you're going to own it with the American people. You're going to own it," Phillips said. "So, for goodness sakes, make sure it's worth the trouble. Make sure it goes far enough in dismantling a law that hurts millions of Americans."

At this point, on the day the Senate measure was introduced, four Republican senators agree with Phillips that the legislation does not, as written, constitute a true repeal of the ACA. Sens. Ted Cruz, Rand Paul, Ron Johnson, and Mike Lee say they oppose the current version of the bill.

Still, Phillips thinks that Senate Majority Leader Mitch McConnell will be able to get an Obamacare repeal bill passed.

"I would never underestimate Mitch McConnell's ability to get something through the Senate," Phillips said. "It would not be surprising to see him get to 50 votes. We are urging them to go big with this, though."

What's "big" to AFP and Phillips? "Actually roll back Obamacare. Actually do that," Phillips said. "And don't worry about having a bunch of subsidies in there. And tax credits are subsidies."

For more from Phillips' conversation with CBS News Chief White House Correspondent Major Garrett and CBS News Political Director Steve Chaggaris, including a spot-on Morgan Freeman-giving-Trump's-inauguration-speech impersonation, listen to "The Takeout" podcast, available on iTunes, Google Play, Stitcher,Spotify and CBSNews.com. And follow "The Takeout" on Instagram, Facebook and Twitter: @TakeoutPodcast.

Producers: Arden Farhi, Nick Fineman, and Katiana Krawchenko