Obama advisor: 'We'd love to work with Republicans'

President Barack Obama's budget proposal "reflects his value of middle-class economics," White House chief economics advisor Jason Furman told CNBC on Monday.

"We'd love to work together with Republicans to invest in infrastructure. We need to a way to pay for that infrastructure," Furman said on "Squawk Box," shortly after the release of the president's $3.99 trillion budget for fiscal year 2016. The fiscal blueprint included a call for higher taxes on companies and the wealthy to boost the fortunes of middle-class Americans and overall economy.

Reviving a long-running debate about corporate tax avoidance, Obama is targeting a loophole that lets companies pay no tax on earnings held abroad. He wants a one-time, 14 percent tax on an estimated $2.1 trillion in profits piled up abroad over the years by U.S. multinational companies. The $238 billion raised from that one-time tax would fund improvements to roads, bridges, transit systems and freight networks.

Read MoreObama proposes $3.99T budget

"It's really an attempt to balance the need to make sure we're not eroding our tax base, but also make sure our companies are competitive as they operate around the world," said Furman, chairman of the White House Council of Economic Advisers.

"I think it's aggressive but not outside the range of reasonableness," said Dan Senor, former advisor to Republicans Mitt Romney, Rep. Paul Ryan, and George W. Bush. "I think it's going to be tough. But what I am stuck by is Ryan was signaling ... after the State of the Union there could be a discussion." The Wisconsin Republican Ryan is now the chairman of the powerful tax-writing House Ways and Means committee.

Steven Rattner, former head of the Obama administration's Auto Task Force, was more dubious—telling CNBC, "The probability of anything actually happening is approximately zero."

Read MoreObama's budget sets up fight with GOP

Currently, foreign earnings are supposed to be taxed at a 35 percent rate, but many companies avoid that through the loophole that defers taxation on active income that is not brought into the United States or repatriated. The president is also seeking to impose a 19 percent tax on U.S. companies' future foreign earnings.

"The 19 percent is actually in some ways more significant because what it means is for the first time we're going to tax foreign earnings whether they come back here or not," said Rattner, chairman of Willett Advisors, which manages the philanthropic assets of Michael Bloomberg.

"That is the lightning rod," Senor, co-founder of the Foreign Policy Initiative, told CNBC. "It just can't be a pinprick strike."

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—Reuters contributed to this report.