He was less specific about a rate target for individuals. Camp, chairman of the House Ways and Means Committee, has proposed a top rate of 25 percent, down from today's 39.6 percent.
"Look, it's hard, because there are a lot of provisions that people like a lot, whether it's charitable deduction or mortgage or state and local, whatnot," Baucus said. "But, still, I do believe that we can dramatically simplify the code."
Baucus said his committee's work on taxes will proceed on a parallel track with a bipartisan budget conference, which is scheduled to conclude by Dec. 13. The Finance panel could provide numbers to the budget group.
Baucus, who has served in the Senate since 1978 and isn't running for a seventh term next year, supports using tax-code changes to raise additional revenue, though less than other Democrats favor.
Earlier in the year, he had said he planned to have the committee consider a bill, what is known as holding a markup, "this fall."
"I can't give a date on markup," he said. "But we have to move quickly, because time is soon not becoming our friend."
He also said he expects the Senate to confirm John Koskinen this year as the next commissioner of the Internal Revenue Service.
The tax agency, under congressional scrutiny for its treatment of tea party-affiliated groups, has lacked a confirmed commissioner since November 2012. Obama nominated Koskinen, a former chairman of Freddie Mac, in August.
On the Patient Protection and Affordable Care Act, also known as Obamacare, Baucus said he has "spent a lot of time" pressing administration officials, including White House Chief of Staff Denis McDonough, on implementation.