The IRS does have the power to have the State Department revoke your passport for owing back taxes is YES. Recently the Fifth Circuit upheld the constitutionality of the government restricting international travel for James Franklin due to back tax debts of $55,000. Mr. Franklin had claimed that revoking his passport had violated his 5th Amendment rights to due process. Luckily, the US is a big country, so you can still have some places to go while all those IRS notices are building up in your mailbox.
Revoking your passport is not the only tool in the IRS toolkit that goes beyond liens and levies. In 2014 Congress passed the Consolidated and Further Continuing Appropriations Act that prohibited federal agencies from awarding contracts or grants to contractors with any amount of delinquency in federal taxes. This law does not get used consistently, but it is another good reason to avoid getting in the hole with the IRS.