Democrats, such as Sen. Charles SchumerCharles (Chuck) Ellis SchumerGOP lawmaker: Dems not standing for Trump is 'un-American' Trump called for unity — he didn’t even last a week Overnight Defense: GOP plays hardball by attaching defense funding to CR | US reportedly drawing down in Iraq | Russia, US meet arms treaty deadline | Why the military wants 6B from Congress MORE (N.Y.), have called on GOP leaders to "abandon" the Tea Party movement — which Schumer has labeled "extreme" — and cut a deal with centrists on a government funding bill. Republicans and Democrats are now working on an agreement that would reduce this year's spending by around $33 billion, though GOP leaders have said there is no deal yet.

McConnell said the Tea Party's goals of repealing President Obama's healthcare law, cutting spending and reforming Washington are not extreme.

“Doesn’t sound extreme to me," he said. "In fact, if you ask me, the goals of the Tea Party sound pretty reasonable."

One of the provisions in the House GOP bill cutting spending by $61 billion this year would defund the healthcare law. Given conservative demands that the language be retained in a final bill, this will be one of the trickier parts of the negotiations between GOP and Democratic leaders who are trying to forge an agreement on this year's spending.

Vice President Biden met with Democrats on Wednesday night and suggested the sides were getting closer to a deal. 

"I think we’re making good progress. We’re all working off the same number now," Biden said. 

But Tea Party groups are not giving up. A coalition of organizations is staging a rally near the Capitol building Thursday afternoon "challenging Congress and the members it helped sweep into power to take swift action on the budget." 

The event features five House GOP lawmakers who are favorites of the movement, such as Reps. Michele BachmannMichele Marie BachmannBachmann won't run for Franken's Senate seat because she did not hear a 'call from God' Billboard from ‘God’ tells Michele Bachmann not to run for Senate Pawlenty opts out of Senate run in Minnesota MORE (Minn.), Steve King (Iowa) and Mike Pence (Ind.).

Despite a recent poll that showed their popularity has reached a low point, Tea Party groups are also exerting their influence over other fiscal issues, such as the debt limit and a long-term budget.

"Thanks to everyday Americans like these getting involved, speaking their minds and advocating for common-sense reforms, I’m increasingly confident we’ll get our fiscal house in order," McConnell said. "And Republicans are determined to do our part to advance the goals I’ve mentioned."