Encontrei a solução. Estavam faltando dependências no pom.xml, vejam como ficou:
<dependencies>
<dependency>
<groupId>org.jboss.spec.javax.faces</groupId>
<artifactId>jboss-jsf-api_2.1_spec</artifactId>
<scope>provided</scope>
</dependency>
<dependency>
<groupId>javax.enterprise</groupId>
<artifactId>cdi-api</artifactId>
<scope>provided</scope>
</dependency>
<dependency>
<groupId>javax</groupId>
<artifactId>javaee-api</artifactId>
<version>7.0</version>
<scope>provided</scope>
</dependency>
<dependency>
<groupId>org.hibernate.javax.persistence</groupId>
<artifactId>hibernate-jpa-2.1-api</artifactId>
<version>1.0.0.Draft-16</version>
<scope>provided</scope>
</dependency>
<dependency>
<groupId>javax.transaction</groupId>
<artifactId>javax.transaction-api</artifactId>
<version>1.2</version>
<scope>provided</scope>
</dependency>
<dependency>
<groupId>org.hibernate</groupId>
<artifactId>hibernate-core</artifactId>
<version>4.3.10.Final</version>
<scope>provided</scope>
</dependency>
<dependency>
<groupId>org.hibernate</groupId>
<artifactId>hibernate-entitymanager</artifactId>
<version>4.3.10.Final</version>
<scope>provided</scope>
</dependency>
<dependency>
<groupId>org.jboss.resteasy</groupId>
<artifactId>resteasy-jaxrs</artifactId>
<version>3.0.10.Final</version>
<scope>provided</scope>
</dependency>
<dependency>
<groupId>org.jboss.resteasy</groupId>
<artifactId>resteasy-multipart-provider</artifactId>
<version>3.0.10.Final</version>
</dependency>
</dependencies>
Acredito que as mais importantes eram as do resteasy. Após colocá-las no pom, tem que dar um validate no projeto novamente para as dependências instalarem. Espero que isso ajude alguém.