Sen. Ted Cruz wants to slash taxes even more deeply than many of his Senate GOP colleagues.
The Texas Republican on Friday called for an "unapologetic tax cut" in the plan Republicans are hashing out and hope to pass this year.
"I think we should be going much bigger and bolder" than the $1.5 trillion tax cut allowed in the budget resolution the Senate is expected to pass next week, Cruz told CNBC's "Squawk Box."
Late last month, Republicans released a framework for the tax proposal, which still lacks many key details. Already, the potential budget deficit created by chopping individual and corporate rates without corresponding tools to raise revenue has raised concerns among some Republicans.
Budget reconciliation rules allow the GOP to pass a tax plan without Democratic votes. But to use the rules, the plan cannot increase the long-term deficit by more than a predetermined amount, without taking economic growth into account.
Cruz said "nobody" cares more about the deficit than he does. But he argued that Republicans should push for even deeper tax cuts to create more growth that will make up for lost revenue.
"I think this should be an unapologetic tax cut," Cruz said. "Not just tax reform, but a real tax cut to generate economic growth."
Cruz joins fellow fiscal conservative Sen. Rand Paul, R-Ky., in calling for deeper tax cuts. Paul has expressed concerns about an independent analysis that estimated that more than a quarter of middle-income Americans would eventually pay more under the plan.
Sen. Bob Corker, R-Tenn., has notably said he does not want to support a bill that increased the budget deficit. Corker, a frequent thorn in President Donald Trump's side, is not running for re-election next year.
Top White House officials have argued that the tax plan will pay for itself with economic growth. However, it is unclear if economic growth will be enough to make up for the major reductions in revenue.
Cruz, who lost the 2016 GOP presidential nomination to Trump, also told CNBC he expects a tax bill to get passed late this year or early next year.