WASHINGTON — A split developing between House Republican leaders and some Senate counterparts who are increasingly open to extending the expiring Bush-era tax cuts only for the middle class is adding to pressure on Speaker John A. Boehner to cut a deficit reduction deal with President Obama.

Senate Republican aides said Friday that Senator Mitch McConnell of Kentucky, the Republican leader, sounded out his Senate Republican colleagues Thursday on a plan to extend the expiring tax cuts for incomes under $250,000, while attaching some Republican priorities like low tax rates on capital gains, dividends and inherited estates.

Leadership aides emphasized that Mr. McConnell was not advocating any specific plan, nor was he saying that extending the middle-class tax cuts was the only option to resolve a potential fiscal crisis next month when hundreds of billions of dollars in tax increases and automatic spending cuts are scheduled to kick in.

“Senator McConnell does not advocate raising taxes on anybody or anything,” Don Stewart, a McConnell spokesman, said Friday. “Despite the president’s failure to lead or to offer any real solutions to the last four years of trillion-dollar deficits, Republicans will continue to look for ways to protect American families and jobs while strengthening entitlement programs.”