No, it won't cause her any problems. Liz Cheney probably angling for House Speakership if Republicans get the House back in 2022 and they will get it back if Biden falls for these ultra leftist Legislations particularly House Democrats proposing.
That 100 Trillion Relief Bill, the new Green Deal, D. C. Statehood, etc.
That is going to fire up a lot of Republicans and not just Trump Supporters but also #NeverTrumpers as well.
That Democratic Congressional Majority in both Houses will be very shortlived I can guarantee you that if Biden/Pelosi/Schumer bow to the wishes of the Progressive Wing of their Party. Heck, that's gonna be a great fun to watch as a Republican the next four years. I almost want them to go full bore left 2021 and 2022 if they control Washington so that we can rebound.
Coming back to your Question I would like Liz to become Speaker and not boring Kevin McCarthy. Kevin doesn't have the guts to do it.