The Tea Party’s future as an influential Washington player is at stake in the showdown over the debt limit and federal budget.

If Democrats and establishment Republicans seal a deal without making any major changes to the new Affordable Care Act, the battle over the debt limit and reopening the government could marginalize the Tea Party as a force within the government, if not the country.

Tea Party leaders vehemently disagree. A deal without significant changes in the Affordable Care Act, or Obamacare, would energize them even further, said Jenny Beth Martin, Tea Party Patriots co-founder. “If they cut a deal that does not include Obamacare, you’ll see us more organized than ever for the next election,” she said.

Perhaps, but polls show the Tea Party-driven shutdown already hurting Republican prospects. Gallup found Republicans are now viewed favorably by 28 percent of Americans, down 10 percentage points from last month. An NBC-Wall Street Journal survey last week found one in five called themselves Tea Party backers — and 70 percent did not.

As the budget showdown tipped into a third week, it evolved into a fight over federal spending — Republicans want to cut spending as already planned in law next January while Democrats want to increase spending.

The White House and congressional Democrats have tried to build public pressure by branding severe cuts as a Tea Party-inspired crusade that will mean pain for those who most need help. Republicans counter that tough steps are needed to slow the growth of the nation’s $16.7 trillion debt.

Sink the Tea Party, the Democratic thinking goes, and establishment Republicans will be unshackled and inch closer to the Democrats’ budget number.

Democrats were pressing on several fronts.

They mounted challenges on the floor of the House of Representatives to get a vote to reopen the government — a vote likely to succeed — only to be turned away by Republicans who control the chamber.

In the Senate, Majority Leader Harry Reid, D-Nev., talked about the “Tea Party Government Shutdown” and maintained that the movement has “the same philosophy as the early anarchists.”

A lot of Republicans are quietly pleased that the Tea Party is at the center of this turmoil.

They don’t like the threat of primary challenges. They recoil at the kind of hard line offered by Martin and want a more collegial approach.

‘Willing to deal’

“At the end of the day, I’m willing to help deal with this,” Rep. Tom Cole, R-Okla., who is close to House Speaker John Boehner, R-Ohio, said of working with others on funding and debt limit.

Boehner stands to benefit from a diluted Tea Party.

He built his political reputation as a consistent conservative who was also a dealmaker. He was at first reluctant to link defunding Obamacare with keeping the government open, but under conservative pressure agreed to do so.

He became a determined advocate for requiring defunding as part of any government spending plan, though his debt limit plan last week did not include any Obamacare link.

Diehard conservatives were not pleased. Should most of the health care law survive, said Rep. Tim Huelskamp, R-Kan., anyone pushing such a deal “would seriously jeopardize their future chances of becoming elected leadership in the House.”

Establishment Republicans, though, believe the hardliners cost the party a huge opportunity to rail against Obamacare.

The day the law’s new health exchanges began operation, Oct. 1, was also the shutdown’s first day. The exchanges were plagued by embarrassing glitches — but the chaos was dwarfed in the media by the shutdown. Obama held an unusually lengthy news conference a week later, and virtually all the questions concerned the shutdown, not the exchange problems.

The risk for Democrats and like-minded Republicans is that they’ll create the kind of establishment steamroller that helped spur the Tea Party movement four years ago. And their big cause, weakening Obamacare, will remain alive.

Martin called suggestions that the movement’s reputation is at stake “bizarre,” and noted that “the reason we got involved [in the current controversy] was Obamacare.”

Chances are Obamacare, along with opposition to what she calls amnesty for undocumented immigrants, will be her message months from now, and a big audience will listen. But they may not be influencing policy in Washington.