"There's a few chapters before we get to the last one. So it's up to us to connect the dots first," RNC chairman Reince Priebus told reporters when asked about impeachment ahead of a New Hampshire GOP fundraiser.
Some conservatives have compared recent IRS wrongdoing to the Watergate scandal, and Rep. Michele Bachmann, R-Minn., last week raised the prospect of impeachment.
"There isn't a weekend that hasn't gone by that someone says to me, `Michele, what in the world are you all waiting for in Congress? Why aren't you impeaching the president? He's been making unconstitutional actions since he came into office,'" Bachmann said during a Washington news conference with tea party leaders.
Paul, a tea party favorite who is considering a 2016 presidential bid, said such rhetoric is premature.
"We need to figure out the truth of what happened before we go anywhere else," Paul said, standing at Priebus' side.
The Internal Revenue Service has acknowledged inappropriate scrutiny of tea party groups applying for tax-exempt status ahead of the last election.
White House chief of staff Denis McDonough and other senior presidential advisers knew in late April that an upcoming report was likely to find that IRS employees had targeted conservative political groups. The White House said McDonough and the other advisers did not tell Obama about the impending report, leaving him to learn the results from news reports later.
The issue has given conservatives a new rallying cry following a disappointing 2012 election cycle. But some GOP leaders worry their criticism could backfire if it appears their attacks appear too politically motived.
While striking a moderate tone on impeachment, Paul said Monday that it "stretches credulity" to think no one else in the Obama administration knew about the misconduct.
"For goodness sake, somebody's got to be fired, if not go to prison," he said in an evening speech to roughly 500 New Hampshire Republicans gathered in the state capital.
Priebus blamed Obama for creating a culture of political "guerrilla warfare" that allowed politics to infiltrate the IRS.
"I think this is just the beginning. It's certainly not the end," Priebus said. "And I'm sure there's going to be a lot more to it. We'll see how far it goes. We'll see how high it goes, too."