To say that a voter cares whether or not a given politician is a liar, is to say that even if the politician is of that voter’s own political party, the voter will reject the politician for being a liar.
In the United States, most voters are either Democratic or Republican; and, for example, Republicans accept George W. Bush (he left office in 2009 with a Republican approval rating of 75%, but a Democratic approval rating of 6%) even though he lied us into invading Iraq, and Democrats accept Barack Obama (his latest approval rating is 90% from Democrats but 11% from Republicans) even though he tried to lie us into invading Syria and was stopped only when British intelligence warned David Cameron and leaked to Seymour Hersh that the 21 August 2013 Syrian sarin attack which Obama was using as a pretext for his planned invasion had been done by the jihadists that Obama was arming, not by Assad as Obama was falsely claiming.
An independent American investigation found exactly he same thing. And Obama knew that if he couldn’t get Britain in on the invasion, the invasion would need to be cancelled. And, as things turned out, he couldn’t get Britain in on it. Cameron didn’t want to become another Tony Blair.