WASHINGTON — Militants for the Islamic State in Iraq and Syria have traveled to Mexico and are just miles from the United States. They plan to cross over the porous border and will “imminently” launch car bomb attacks. And the threat is so real that federal law enforcement officers have been placed at a heightened state of alert, and an American military base near the border has increased its security.

As the Obama administration and the American public have focused their attention on ISIS in recent weeks, conservative groups and leading Republicans have issued stark warnings like those that ISIS and other extremists from Syria are planning to enter the country illegally from Mexico. But the Homeland Security Department, the F.B.I. and lawmakers who represent areas near the border say there is no truth to the warnings.

“There is no credible intelligence to suggest that there is an active plot by ISIL to attempt to cross the southern border,” Homeland Security officials said in a written statement, using an alternative acronym for the group.

Democrats say opponents of President Obama are simply playing on concerns about terrorism as part of their attempt to portray Mr. Obama as having failed to secure the border against illegal immigration.