Republicans passing a tax reform bill would be nice for stocks, but strong earnings are really what will take the market higher, closely followed strategist Bob Doll told CNBC on Thursday.

Tax reform “is important, but it’s not the whole ball game,” said Doll, Nuveen Asset Management’s chief equity strategist. “The ball game is earnings. And earnings have kind of been off the charts. And that’s why stocks have gone up 40 percent in the last 20 months.”

U.S. stocks were higher on Thursday after falling in their previous two sessions. The Dow rose more than 150 points after Dow components Cisco and Wal-Mart reported better-than-expected quarterly earnings.

“Yeah, the tax bill would be icing on the cake, no doubt about it,” Doll told “Squawk Box.” “I think Republicans know if they don’t do something it is a political suicide.”

The Senate unveiled their tax reform plan last week, and the House is expected to vote on their version of the bill later on Thursday. On Wednesday, GOP Sen. Ron Johnson said he would not back the Senate plan in its current form. Republicans hold only a two-seat majority in the Senate, so the GOP has little margin for defections because Democrats are uniformly opposed to the plan.

“They have to come together,” Doll said. “If it’s a simpler bill, watered down from what it is … and the president will sign whatever comes across his desk.”

Doll predicts the plan will take some “tinkering” and Republican lawmakers won’t pass a bill until next year. “I don’t think anything happens this year. A lot of noise,” he said. “They can’t lose too many votes.”

Regarding the market, Doll said there will be some down months along the way, but believes, “we’re shifting from a gallop-higher market to a grind-higher market.” The bull market is not over, he added, because “the earnings environment is still good.”