The Fix notes that a vast majority of Americans blame the Republicans for the shutdown:

Disapproval of congressional Republicans’ budget wrangling after a weeklong shutdown has shot up to 70 percent, with 51 percent disapproving “strongly,” according to a new Washington Post-ABC News poll.

Even in crimson Utah, The Deseret News ran a poll that doesn't look very good for Republican chances to save face out of all this:

SALT LAKE CITY — A majority of Utahns don't believe it was worth shutting down the federal government to fight President Barack Obama's new health care law and most blame Republicans just as much as Democrats, according to a new Deseret News/KSL poll.

If even Utahns blame Democrats and Republicans equally right now, I guarantee a majority of people in red states will blame Republicans for the shutdown if this thing goes on much longer.