WASHINGTON — A raft of new polls, all reporting fairly similar numbers, underscores two critical facts about where the presidential race stands: President Barack Obama has emerged from the back-to-back conventions having erased the edge that Republican challenger Mitt Romney had enjoyed on the economy and holds a small, but consistent, lead.

The Gallup, ABC/Washington Post, CNN/ORC and Rasmussen surveys showed Obama with between 48 percent and 52 percent of the vote in a hypothetical matchup with Romney. The Republican’s strength varied between 44 percent and 48 percent. Obama appears to have gained about three percentage points after the Democratic convention, while Romney gained little, if any, ground after his convention.

Some years, a candidate’s support rises in polls after his convention but then fades. In other years, however, the increase becomes a lasting part of the race. A three-point gain would put Obama in about the same position as George W. Bush in the 2004 campaign. In Gallup’s surveys, Bush gained two points after his 2004 convention, took a small lead over the Democratic nominee, Massachusetts Sen. John F. Kerry, and held it for the rest of the fall campaign.

Through most of the year, Romney has enjoyed a significant edge as the candidate voters think would be better at handling the economy. Romney’s campaign has been pretty much built on the assumption that voters will view him that way.

In these post-convention surveys, however, that edge has disappeared. In the ABC/Washington Post poll, for example, Obama now leads on that question, with 47 percent of registered voters saying he would be better, compared with 45 percent siding with Romney. In the CNN/ORC survey Obama held a one-point lead on that question.

A tie on the question of economic stewardship would be an important advantage for Obama because he leads on most other questions testing candidate attributes. Polls consistently have shown that voters rate him more highly than Romney on handling foreign affairs, for example. Similarly, he leads when voters are asked questions about empathy. In the ABC/Washington Post survey, for example, Obama held a 10-point edge on the question of which candidate “better understands the economic problems people in this country are having.”

Some of the new surveys, most notably the ABC/Washington Post poll, showed a gap between Obama’s lead among all registered voters and those deemed likely voters. In that survey, Obama led 50 percent to 44 percent among registered voters, but 49 percent to 48 percent among likely voters.

That gap illustrates the importance that turnout-and particularly the racial makeup of the turnout-likely will play in the election results.