President Obama's signing statement defying legislation limiting his ability to employ "czars" should give Republicans pause before striking an agreement with him again, a senior GOP lawmaker said Tuesday evening.

Rep. Tom Cole (R-Okla.), a member of the House Appropriations Committee, urged Republicans to take strong action to defend provisions in their agreement to fund the government for the rest of the 2011 fiscal year that would have denied Obama the ability to use funds to pay for the informal advisers, or "czars," he's used in his administration.

Obama on Friday issued a signing statement, a determination of constitutional interpretation attached to a bill he signs into law, notifying Congress that he had determined the limits on czars were unconstitutional, and that he would disregard that provision.

"Remember, this was a mutually agreed-upon document," Cole said on the conservative Hugh Hewitt radio show. "So for them to break their word within a week afterwards, I think, would raise questions about any other deal that you manage to arrive at with them."

The measure on czars was part of the final legislation negotiated by Obama, House Speaker John Boehner (R-Ohio) and Senate Majority Leader Harry Reid (D-Nev.). While the provision to defund czars was hardly one of the biggest riders attached to the spending bill, a group of Republicans has loudly and consistently protested Obama's employment of the informal advisers, who aren't subject to congressional oversight or Senate confirmation.

Cole said he wouldn't "telegraph" how he thinks Republicans ought to respond, adding that he would defer to leadership to make any decision as to how to enforce the czar ban.

"We still have the budget item, and I think we ought to use it," Cole said.