Homeland Security Director Tom Ridge met personally with Sen. Robert Byrd, D-W.Va., Wednesday to discuss ways to end their disagreement over Ridge's refusal to testify before the Senate Appropriations Committee that Byrd chairs.

White House and Capitol Hill sources said all sides described it as a "good meeting." Sources said Ridge promised to take Byrd's concerns "directly to the president."

Democrats, particularly Byrd, insist Ridge testify before a Senate committee about his activities. They refuse to strike an alternative arrangement, but Byrd has said he is not thinking of subpoenaing Ridge, which would force him to testify.

Ridge and the White House have argued that as a presidential adviser, Ridge is not obligated to testify before Congress. President Bush has asked for $38 billion for homeland security funds, but Ridge is not in charge of the money nor any agency except for a small staff.

Senate Majority Leader Tom Daschle, D-S.D., said Thursday that congressional relations with the White House are "not as good as they could be" because of the administration's refusal to allow Ridge to testify.

"It is so critical when you make a request for $38 billion dollars in that somebody ought to come up to explain [where/how the money will be used]," he said.

Sources say White House Chief of Staff Andrew Card told Daschle on Wednesday that Ridge would be available to brief all 100 senators and take questions Wednesday at 2:30 p.m. in a secure conference room in the Capitol.

Daschle, sources say, turned the offer down calling it the "wrong time." The Senate was debating campaign finance reform. That legislation passed 60-40 after a daylong debate that capped a seven-year push.

Daschle has refused to accept other previous offers by the administration for "secret briefings."

"This shouldn't be secret," Daschle said Thursday. "We'll just have to find a way, hopefully without coercion, to get this done."

Sources say several Republican senators have urged Ridge to modify his opposition and agree to testify before Congress. Ridge has indicated that he and the administration are trying to work out a deal to end the flap.

Republicans, Democrats and White House sources all predict that the impasse will soon be resolved. Democrats, who seemed to be spoiling for a fight a few days ago, now downplay the flap and express confidence that a deal is near.

Fox News' Julie Asher contributed to this report.

Carl Cameron currently serves as Fox News Channel's (FNC) Washington-based chief political correspondent. He joined FNC in 1996 as a correspondent.