A push by President Obama to cut deals in the Senate is likely to put increased stress on relations between House Minority Leader John A. Boehner and his Senate counterpart, Mitch McConnell .

While McConnell, R-Ky., quickly opened quiet talks with the new White House on a range of issues, Boehner, R-Ohio, has taken a tougher approach and has recently moved with mixed success to begin a dialog with Obama. The president met with leaders of both parties Jan. 23 and plans to discuss the stimulus with Republicans during a visit to Capitol Hill on Tuesday.

Obama’s plan is to begin his term with bipartisan legislation that could help generate momentum for his most difficult objectives — overhauls of health care and entitlements. But it remains unclear whether Obama will press for deals with Republicans in both chambers or focus instead on the Senate, where some bipartisan support will be essential.

Senior Republicans say Boehner and McConnell share a low-key managerial style, but that their differences may be highlighted when they confront a Democratic administration. A longtime appropriator, McConnell has long pushed for deals on big spending measures such as the stimulus. Boehner, leading a caucus that has grown more conservative, has taken a harder line on curbing domestic spending.

“Mitch knows that on any given vote, he can influence the process through the use of the filibuster. John doesn’t have the filibuster. His job is difficult because he faces the constant challenge to boost morale. I mean, it’s not fun to lose every time,” said Sen. Richard M. Burr , R-N.C., the chief deputy whip to McConnell, a former House colleague of Boehner, and a friend of both.

Boehner and McConnell play down such differences and stress their intent to work in tandem. But McConnell said some conflicts are inevitable. “The Senate and the House are not exactly the same. And you know I wouldn’t predict that on every single issue, we would mirror . . . each other,” he said.

“Mitch and I have a good relationship. It’s a working relationship. I like and respect him,” Boehner said. “We have not been on different sides of many issues over the last few years.”

But their priorities were not the same in the last Congress. Although both leaders backed President George W. Bush ’s effort to dictate a cap on discretionary spending, McConnell tried to salvage spending bills and supported the 2008 farm law rewrite (PL 110-246) that Boehner opposed and Bush unsuccessfully vetoed on grounds it was too costly. Although both leaders back disclosure of earmark sponsorship, McConnell takes pride in funding home-state projects, while Boehner does not request earmarks.

Last fall, McConnell cut an early deal with Senate Majority Leader Harry Reid , D-Nev., that paved the way for Senate passage of the financial industry bailout requested by the Bush administration (PL 110-343). That increased pressure on Boehner, whose caucus generated significant opposition to the package, to give ground.

Similar differences arose this month. While Boehner attacked the new administration’s plan for managing the bailout, McConnell praised Obama for negotiating in good faith on the release of the second half of the $700 billion rescue package. Six Senate Republicans joined Democrats to defeat, 42-52, a measure (S J Res 5) that would have blocked the additional funding.

And McConnell’s criticism of the Democrats’ stimulus proposal has been limited to suggesting more tax cuts and the use of loans instead of grants to states. Boehner has hinted at strong House GOP opposition while calling for Republican-backed tax breaks and less spending.

Different Styles

Differences between Boehner and McConnell pale in comparison with other notable GOP leadership tiffs. Speaker J. Dennis Hastert of Illinois and Senate Majority Leader Bill Frist of Tennessee clashed over the 2003 tax cuts (PL 108-27). And Speaker Newt Gingrich of Georgia antagonized Senate Majority Leader Bob Dole of Kansas by forcing a government shutdown battle with President Bill Clinton.