WASHINGTON – Congress and the White House appear no closer to an agreement on the year-end budget crisis, although House Speaker John A. Boehner and President Barack Obama have opened lines of communication that could produce a deal later this month.

The president on Thursday enlisted a Virginia family to humanize his effort to preserve tax rates for low- and middle-income households while raising them on the wealthiest 2 percent of Americans. Republicans are fighting to keep the lower rates for everyone.

The Santana-Massenburg family of Falls Church, Va., would be snared if Washington failed to find agreement. All lower tax rates are set to expire Dec. 31, resulting in a $2,200 tax increase for average Americans.