McDonough met with nine Republicans as part of a White House effort to avoid a showdown over raising the national debt ceiling later this year, The Hill reported Wednesday.
McDonough characterized the meeting as "a good conversation" but some Republicans were less than enthusiastic about prospects for a deal.
One source familiar with the meeting told The Hill that most of it was spent debating how bad the nation's budget picture looks.
"The intensity is not where it needs to be right now," said Sen. Bob Corker, R-Tenn., as he walked into the Tuesday afternoon meeting.
Sen. Johnny Isakson, R-Ga., said "great discussions" were needed.
White House officials and lawmakers hope to meet weekly or more frequently, said Sen. Ron Johnson, R-Wis.
Other Republicans at the meeting were Sens. Kelly Ayotte of New Hampshire, Tom Coburn of Oklahoma, Lindsey Graham of South Carolina, Rob Portman of Ohio, Dan Coats of Indiana and John Thune of South Dakota.