WASHINGTON (AP) _ On Wednesday, John Cox and Daniel Lumley stood beside President Clinton at the White House, held out as victims of the health care system the administration wants to reform.

By Thursday, their cases were at the center of a dispute between the White House and Senate Republican Leader Bob Dole.

Speaking at a rally outside the Capitol for health ''reform riders,'' Vice President Al Gore said Dole's proposal for reform ''simply does not fix the problems of Daniel Lumley and John Cox.''

In a Senate floor speech, Dole swiftly disputed Gore, and said, ''We shouldn't make politics out of people's misery in this place. ...The fact is that our plan would help John Cox, Daniel Lumley and countless other low- and middle-income Americans who find themselves in similar situations.''

Lumley, of Seattle, lost his arm in a motorcycle accident; Cox's wife, Jan, of Athens, Texas, died last week of cancer that went untreated for months because they lacked insurance. Administration aides said she was denied coverage when her condition was diagnosed, and she lived 40 months under this exclusion.

In his remarks, Gore said her illness had been diagnosed ''a week before his new plan took effect, so the insurance company wouldn't cover it....

''Would Bob Dole's plan actually mean no insurance company would deny coverage for pre-existing conditions? No, it would not. Look at it. It just doesn't do it.''

In reply, Dole said his plan does away with these so-called pre-existing condition exclusions, an assertion that was quickly supported by Democratic Sen. Daniel Patrick Moynihan of New York.

In fact, Dole's proposal eliminates this type of exclusion after a phase-in period.

An aide to Dole said that an uncovered individual seeking insurance as part of a group - as Cox's wife would have - could be excluded for up to six months, under Dole's proposal. The insurance plan would then have to provide coverage.

But Dole also would require states to have a one-time, 90-day open enrollment period during which individuals could apply to insurance plans without being subjected to pre-existing condition limitations.

Other prominent bills contain similar provisions, although the details differ.

Senate Majority Leader George Mitchell's bill also would allow policy writers to deny new applicants coverage for up to six months on the basis of a pre-existing condition, but only through 1996. A three-month denial would be permitted from 1997 through 2002.

The Democratic leadership bill pending in the House has the six-month exclusion for coverage based on pre-existing conditions, too, through 1998. Beginning in 1999, no exclusions would be allowed.

Addressing Lumley's case, Gore said, ''Lumley had a motorcycle accident. He needed a lot of care. He hit his lifetime limit and so his insurance ran out. But his health bills kept on coming. He was able to get a lesser policy but he lost that insurance when he lost his job. Now he's in debt and afraid that when he takes a job he'll once again lose his coverage....

''Bob Dole says his plan would take care of it, but it does not fix the problem of lifetime limits at all...''

Dole's aide said his plan does not permit insurance companies to limit the benefits paid out over an individual's lifetime. Aides to Mitchell and House Majority Leader Richard Gephardt said their bills were similar in that respect.

On another issue raised by Gore, affordable insurance, there are differences.

Dole's bill does not require insurance companies to offer a prescribed set of benefits. Different bills sponsored by Mitchell and Gephardt impose such a requirement.

Dole's bill also has less generous subsidy provisions for low-income individuals than either of the Democratic alternatives.