Senate Republicans delayed the vote on their health-care bill on Tuesday, but economist Austan Goolsbee told CNBC he believes the measure is doomed.

The vote on the Obamacare replacement bill has been pushed back to after July 4 due to opposition from enough GOP members to block the legislation.

Goolsbee told "Power Lunch" the real issue is the tax cuts included in the measure. According to a new analysis by the Urban Institute and the Brookings Institution's Tax Policy Center, about 45 percent of the benefits from those cuts will go to households making $875,000 or more.

"That's going to kill this bill," said Goolsbee, who served on Obama's Council of Economic Advisors. "It's a massive tax cut for millionaires. It's high-income people's capital gains tax rates going down."

While Republicans will have to try to change the narrative in order to sell the bill, "the only problem is those are the facts of the bill," he pointed out.

"The worst thing that can happen to Republicans is that people actually just read this. If they read it, the opposition is going to be even bigger than the massive opposition that's already there."

On Tuesday, Senate Majority Leader Mitch McConnell said leaders will continue discussions within the conference and will work toward getting at least 50 people "in a comfortable place." He said he's still "optimistic" about passing a plan.

Watch: Mitch McConnell: Working on getting 50 people to support health-care bill