Doesn't necessarily need to be more liberal as the other poster said. Running as democrat lite against the democrats isn't really going to solve much.
Putting my personal feelings aside and looking at it objectively here.
Immigration reform of 2013 was an attempt, a bad one. They tried to just shove it through with no regard for anything else. Hey, we can add on a bunch of Hispanics to our existing base, and we win! Backfired obviously, it also missed the fact that what immigrants care about the most is not immigration, but jobs, healthcare, and education (in that order IIRC).
We've lost 4 of the past 6 elections, one of those was EC only, and the other had the lowest popular vote for an incumbent president ever (50.x). That was a wartime incumbent election, and that was the best we could do.
The GOP has 4 options.
Double down. Call this election a fluke, a perfect storm for outsiders to disrupt everything. Right message, wrong candidates. Move on with Bush clone number 6 next time.
Concede on immigration reform. Conservative, but strong on immigration. It's obviously an issue a lot of people, including a large portion of the base (not talking about Trump specifically here, but the general backlash from Gang of Eight as well) feel strongly about. I don't think this will be enough though, like I said above, there are more important issues immigrants care about.
Realignment. I don't think Trump is leading the charge on realignment as others think. Realignments rarely, if ever happen due to one nominee with so many views that run counter to the party line. Especially if he loses. He crossed the free marketeers with his trade talk, he crossed the anti-tax folks with his progressive tax policies, and he crossed the neocons with his war bashing. The democrat civil rights re-alignment took years of work by 2 different interest groups working within the party to influence and change policy, and get their guys elected. The internet and social platforms may have impacted this though.
But, like I said I'm looking at this objectively, not from my personal feelings. Go center-right. To start, fix Obamacare, instead of repealing. It would be damn difficult, if not impossible to repeal Obamacare at this point anyway. Cut taxes less at the top, more at the bottom. Invest in infrastructure, create the jobs people are looking for. Worry less about regulation on Wall Street, and more about regulations on small businesses. I don't agree with this option, if anything I'd like to see the GOP become more libertarian, but that won't happen.
Last, and most likely. Change the party rules to prevent Trumps from taking over in the future. The GOP is doing fine at the state level and lower. Majority in both houses, state governerships, legislature at almost all levels is republican. Forget the presidency, in a big tent like the GOP it's very difficult to please everyone, and often you end up pleasing nobody. It's nice to have, but not necessary. Is it worth making sweeping changes to be more popular? Fix issues at the state level, and our time will come again in the future. The president can grant illegal immigrants the right to work, but not to vote. Problem with this is, time isn't on our side. Changing demographics, increasing immigrants, increasing youth which is growing older by the year and are by and large liberal, etc.
I don't know what the right answer is. If I did I'd be making a fortune as a consultant right now.