Norquist said the president and the Democrats are holding corporate rate reform hostage. "They will only do corporate tax reform if it's a trillion dollar tax increase."
Two years ago, the White House proposed eliminating tax loopholes and lowering the corporate tax rate from 35 percent to 28 percent. It had also sought to reduce provisions that allow companies to shift income and investment outside the U.S., while giving tax credits to American companies to bring operations back.
The marginal corporate tax rates in Ireland is 12.5 percent, while Britain's is 21 percent. Both are much lower than the U.S., according to KPMG. Few American companies pay the full 35 percent rate because of loopholes, but it's still generally much higher.
"I think the system that makes the most sense is basically what states governments in the United States have done to tax corporations. They've been struggling with the same mobile capital constraints that nations now face," Orszag said in a separate "Squawk Box" interview.
"The thing that's hardest for companies to manipulate is where their sales occur," he continued. "So therefore, if 'X' percent of global sales are in the United States, 'X' percent of your global profits should be taxed in the United States regardless of where you're headquartered. Period."
Pfizer's attempt to buy its U.K. rival AstraZeneca drew the attention and the ire of Washington about these inversion deals, which have largely been in the pharmaceutical and medical industries. Pfizer eventually dropped its bid, which was forced into the open in April.
But there are many other pending megadeals, including medical devices specialist Medtronic's offer to buy Dublin-based Covidien, and AbbVie's bid to acquire Ireland pharma giant Shire.
Read MoreThese deals may suffer in US 'inversion' crackdown