Senate Minority Leader Mitch McConnell on Tuesday joined a weekly closed-door meeting of House Republicans to advocate for protecting the sequester spending cuts in the on-going budget negotiations with the Democrats.

McConnell, R-Ky., also shared his thoughts on what a Senate Republican majority might look like and how it might function and help the GOP control the legislative agenda during the final two years of President Obama's tenure, a source familiar with the discussion said. Senate Republicans need to flip six Democratic-held seats in next year's midterm elections to take control of the Senate.

But the primary focus of McConnell’s talk was about the sequester, a series of automatic, across-the-board spending cuts Democrats want to prevent from taking effect in January. A House-Senate conference committee is negotiating a spending bill to fund the government after Jan. 15, when the existing continuing resolution agreed upon to end October’s government shutdown runs out. The conference committee is supposed to conclude its deliberations by Dec. 15.

McConnell was a lead negotiator of the 2011 financial agreement that raised the debt ceiling but also included multiple spending cuts, include deep cuts at the Pentagon. Obama and Senate Democrats hope to negotiate the elimination of the sequester cuts and increase overall spending in 2014. House Republicans have indicated a willingness to trade sequester cuts for reforms in entitlement programs like Social Security and Medicare, a strategy of which Senate Republicans are suspicious.

The meeting between McConnell, the Senate's top Republican, and House Republicans is not that unusual. House Speaker John Boehner, R-Ohio, has occasionally been a guest at private meetings of Senate Republicans.