President Donald Trump's budget proposal is likely to help produce 1.9 percent economic growth, not 3 percent, former Office of Management and Budget Director Jim Nussle told CNBC on Tuesday.

Nussle's comment came the morning after Trump's proposed fiscal 2018 budget became public. The White House said it is a key component in pushing economic growth to 3 percent.

The Congressional Budget Office currently estimates, however, growth at about 1.9 percent and the Federal Reserve projects the economy will expand at a 1.8 percent annual rate.

"When you say we're going to get to 3 percent growth and then you paint a picture of how you're going to get to 3 percent growth, most economists say that's unrealistic given the current trend line," Nussle, who served under the George W. Bush administration, said on "Squawk Box."

"Over the history, CBO has been closer to being correct on these numbers. Being at 1.9 as opposed to 3 is probably more realistic," he added.

Trump's budget proposal calls for slashing federal spending over the next 10 years through cuts across most agencies, including government safety-net programs. Current Office of Management and Budget Director Mick Mulvaney said that the Trump administration stands by its forecast and that economists are underestimating the benefits.

"That assumes a pessimism about America, about the economy, about the people, about its culture that we're simply refusing to accept," Mulvaney said. "We do not believe that [3 percent] is something fanciful."

Nussle, also a former Republican congressman from Iowa, said if the economy doesn't reach 3 percent growth the Trump administration is likely to blame lawmakers for not pushing through the president's policies.

"So, when they don't pass it and we don't get to 3 percent growth, they're going to say, 'Well that's because you didn't pass my plan,'" Nussle said. "I think that's maybe the reason why they would put it out in this kind of format."

— CNBC's Ylan Mui contributed to this report.