The short answer is no.

There are dozens of major language families throughout the Americas. Algic is the only one found on both the east and west coast of North America, and even the handful of small Algic languages in the west have been isolated from their east coast counterparts for thousands of years and would not be mutually intelligible.

In the Eastern Woodlands alone (mostly the US east of the Mississippi), there are four major language families. Algic is represented by the various Algonquian languages like Ojibwe, Shawnee, Powhatan, and Wôpanâak. Iroquoian languages are represented by Cherokee, Seneca, Mohawk, Wendat, etc. Siouan languages are represented by Catawba and a few others formerly located in Appalachia and the Ohio Valley. Muskogean languages are represented by Creek, Chickasaw, Choctaw, etc. Then we get to the various language isolates like Tunica, Calusa, Timucua, Natchez, and Yuchi that don't have obvious ties to other languages in the area (though some linguists have tried to link Tunica and Calusa together, Yuchi with the the Siouan languages, and Natchez with the Muskogean languages with limited plausibility).

Between each language family there's no hope of mutual intelligibility, except for the occasional loan word that hops from one language to another. It'd be like English and Arabic speakers trying to communicate. Even within each family, it's often like English and Spanish speakers trying to communicate. A few languages though are more closely related - Spanish and Portuguese than Spanish and English. Seneca and Cayuga, for example, are very closely related, as are Choctaw and Chickasaw.