WASHINGTON — After more than a week of tirelessly pressuring Congress to move his top domestic priority, President Barack Obama may have to settle for a fallback strategy on health care overhaul.

Instead of votes in the House and Senate by August, the best Democrats may be able to hope for this summer is action by the full House by the end of the month and some sort of agreement on a bipartisan plan in the Senate before lawmakers head home for vacation.

Not only are Republicans honing their opposition, but some Democrats in both chambers are voicing doubts about moving such complex and costly legislation too quickly.

"No one wants to tell the speaker (Nancy Pelosi) that she's moving too fast and they damn sure don't want to tell the president," Rep. Charles Rangel, D-N.Y., a key committee chairman, told a fellow lawmaker as the two walked into a closed-door meeting Tuesday.

The health care battle is turning into a major test of Obama's leadership. One Republican senator says if the party can stop Obama on health care, it will break him.

In an interview with CBS News on Tuesday, the president insisted on action by lawmakers, even as he conceded some of the criticism was valid. Referring to objections from a group of conservative Democrats in the House, Obama said, "I think, rightly, a number of these so called Blue Dog Democrats — more conservative Democrats — were concerned that not enough had been done on reducing costs."

Obama said those issues can be addressed as the legislation keeps moving forward. Congress has already spent years studying and debating the problems in the health care system, he said.

Meanwhile, a conservative South Carolina Republican, Sen. Jim Demint, refused today to back away from his earlier assertion that the health care overhaul will prove to be Obama's "Waterloo."

Interviewed on NBC's "Today" show, DeMint said the statement was "not personal." But he also said someone must "put the brakes on" Obama, accusing the president of engaging in "a spending spree."

House Democrats put their divisions on display over the details and timing of health care legislation Tuesday. The Democratic leadership juggled complaints from conservatives demanding additional cost savings, first-term lawmakers upset with proposed tax increases and objections from members of the rank-and-file opposed to allowing the government to sell insurance in competition with private industry.

Pelosi, D-Calif., vowed weeks ago the House would vote by the end of July on legislation to meet two goals established by Obama. The president wants to extend health coverage to the tens of millions who now lack it, and at the same time restrain the growth in health care costs far into the future. The upfront costs, however, could reach $1 trillion to $1.5 trillion over 10 years.