In the poll, conducted by Quinnipiac University, 38 percent of those surveyed say they would vote for their Republican House candidate, and an equal number choose the Democrat. Twenty percent are undecided.
That's a slight decline for Democrats since the last poll, released earlier this month, that indicated 41 percent of voters would back a Democrat while 37 percent would back a Republican.
However, Democrats in Congress are still seen more favorably than Republicans, with respect to their job performance and the party generally. While 24 percent of those polled say they approve of the way Republicans in Congress are handling their job, 30 percent approve of Democrats, a steady approval rating for both parties.
Sixty-seven percent of those polled disapprove of Republicans' job performance, while 60 percent disapprove of Democrats.
Americans' opinions of the two parties have improved somewhat since April, however, with those polled viewing Democrats more favorably than Republicans.
Both parties are underwater, but 42 percent of those polled view the Democratic Party favorably, while 47 percent view it unfavorably. Thirty-five percent view the Republican Party favorably, while 50 percent view it unfavorably.
The poll was conducted among 1,419 registered voters from May 22-28 and has a margin of error of plus or minus 2.6 percentage points.