House Speaker John Boehner, R-Ohio, told Republicans in a private meeting Wednesday morning that they should not buckle under pressure from the Democrats to raise income tax rates to avert the so-called fiscal cliff, but should instead keep pushing for spending cuts as well as pro-growth spending and entitlement reforms.

"We've staked out a principled position," Boehner told lawmakers, according to a participant. "It's important that everyone in this room continue to be clear with our constituents about what that position is."

Some in the GOP have begun to waver on the tax issue as President Obama and Democrats push to raise taxes on top income earners - those making more than $250,000 annually.

A day before Boehner urged his lawmakers to hold firm, Rep. Tom Cole, R-Okla, said he was trying to convince those same House Republicans to back Democratic plans to raise some income taxes in the name of compromise and to avert automatic tax increases that could hit lower-wage workers on Jan. 1.

Boehner said he talked to Cole Wednesday morning.

"I told him I disagreed with him," Boehner said. "You are not going to grow the economy if you raise the top two tax rates. It will hurt the economy."

Republicans have already offered to raise additional tax revenue by ending some deductions closing loopholes in the tax code, Boehner noted.

"We are willing to put revenue on the table as long as we are not raising rates," Boehner said.

Boehner was meeting Wednesday morning with Erskine Bowles, a former chief of staff to President Bill Clinton who co-chaired Obama's debt-reduction commission. Bowles supports tax increases, but also steep cuts in federal spending and meaningful entitlement reform.