The tea party never really mattered that much.
You have been led to believe that the tea party drove the Republicans to the right. Not so fast, there, buddy.
In studies of Congress, we measure ideology primarily with scores called "NOMINATE," based on the work of Keith Poole and Howard Rosenthal. You can get the scores at Voteview here. Scores range from -1 at the liberal end to +1 at the conservative end. If you dig around their page, you will also find wonderful graphs like this one.
Basically, what this graph shows is that House Republicans have been getting more conservative steadily since the 1970s. The tea party came onto the scene in 2009. So, you see, the tea party is such a powerful force that its impact rippled back in time and caused the Republican Party to start getting more conservative in the 1970s!!!!!!!!!!!!!
Um, yeah, time and causation don't work that way. Short version: moderate-to-conservative Southern Democrats were replaced by very conservative Southern Republicans while moderate-to-liberal Northeastern Republicans were replaced by liberal Democrats. Then, the conservative Southerners kept getting more conservative for reasons difficult to explain. Grover Norquist, talk radio, Fox News, lizard people, chemtrails, etc. Obviously, some of those are jokes. For example, there is no such person as Grover Norquist. (Let's see if I can start a new conspiracy theory...)
The tea party was the Republicans' reaction to a president they really, really didn't like. It was a mobilization effort. And, in 2009 and 2010, it accomplished exactly jack fucking shit. What was their primary goal, legislatively? To block Obamacare. How'd that work out for them? (For the record, I'm still not convinced one way or another on the likelihood of its repeal).
Then there's the little matter of the 2010 election, and that is where the mobilization efforts of the tea party may have actually mattered. Republicans were really pissed off in 2010. Yup, we're talkin' 'bout piss! The jokes write themselves! Anyway, the 2010 election was an anti-Democratic wave election of historic scale. Whether or not the Republicans' gains would have been as big without tea party mobilization is an impossible-to-test counterfactual, but it is at least worth considering. Remember, though, that midterm elections strongly tend against the party of the presidency. No, they don't intrinsically go Republican, they go against the party of the president. That has meant going Republican in 2010 and 2014 because of a president with a "D" after his name. Pundits have the memories of goldfish. Anyway, combine the fact that the president was a Democrat in 2010 with the fact that the Democrats had two previous cycles of gains in congressional elections and the fact that the House map is strongly biased for Republicans, and we should have expected a Republican House after the 2010 election anyway. So, really, was it the tea party that gave Congress to the Republicans in 2010, or just basic politics? Those mobilization efforts couldn't hurt, but I wouldn't call them determinative.
Which brings us to yesterday's protests. That... wasn't normal. Nothing about the Trump Presidency is normal. Will the protests change the minds of any Republican legislators? No. Will they change Trump's mind about anything? No. See: 2009-10. Will it move the Democratic Party to the left? No. The tea party was never as big a force in moving the Republicans to the right as commentators thought.
If, however, yesterday is truly an indicator of how mobilized the left will remain through 2018, my advice to Republicans is as follows: rush through as much as you can. That clock is ticking.